How would Kant handle errors in our perceptions of the world in his transcendental idealism? If what is external to us is so heavily meditated and contributed to by our mental apparatuses, how do you explain incorrect assessments of these external things? It seems that transcendental idealism falls to the same criticism that marred typical idealism (unless you deny external objectivity altogether).
Regarding the question's claim
There are parts of the Critique of Pure Reason that seem to say exactly what you think. Kant explicitely adresses this in the introduction of his transcendental dialectics (Of Transcendental Illusory Appearance):
In a cognition which completely harmonizes with the laws of the understanding, no error can exist. In a representation of the senses — as not containing any judgement — there is also no error. But no power of nature can of itself deviate from its own laws. Hence neither the understanding per se (without the influence of another cause), nor the senses per se, would fall into error; the former could not, because, if it acts only according to its own laws, the effect (the judgement) must necessarily accord with these laws. In the senses there is no judgement — neither a true nor a false one. (B350)
This seems to mean that there was no room for error. But Kant would not be Kant if it was that easy.
Regarding Kant's answer on these implications
But in accordance with the laws of the understanding consists the formal element in all truth. In the senses there is no judgement — neither a true nor a false one. But, as we have no source of cognition besides these two, it follows that error is caused solely by the unobserved influence of the sensibility upon the understanding. And thus it happens that the subjective grounds of a judgement and are confounded with the objective, and cause them to deviate from their proper determination,* just as a body in motion would always of itself proceed in a straight line, but if another impetus gives to it a different direction, it will then start off into a curvilinear line of motion. To distinguish the peculiar action of the understanding from the power which mingles with it, it is necessary to consider an erroneous judgement as the diagonal between two forces, that determine the judgement in two different directions, which, as it were, form an angle, and to resolve this composite operation into the simple ones of the understanding and the sensibility. (ibid)
*Sensibility, subjected to the understanding, as the object upon which the understanding employs its functions, is the source of real cognitions. But, in so far as it exercises an influence upon the action of the understanding and determines it to judgement, sensibility is itself the cause of error.
There are two main points:
Sensibility and Understanding may part ways the moment our sensibility does affect our understanding not in accordance with the laws of the understanding. So to say, in a way the understanding does not necessarily compute "correctly", i.e. according to the "laws" of sensibility. It may be a good guess, so to say, but there are errors possible.
As the only source of "truth" are the laws of understanding (as our only accesss to "reality" is through our understanding), the source of "error" has to be in our sensibility.
Summary and conclusion
To sum it up, the source of the error lies in the play of our faculties/powers of knowledge [Spiel der Erkenntnisvermögen/Erkenntniskräfte], and the place is in the synthesis of the manifold under concepts, where the understanding tries to compute the input of sensibility in a way so that it falls under the laws of understanding, i.e. to make sense of it. This always has a momentum of spontaneity (see B129-30) as soon as they do not correspond directly.
And if this "making sense", like seeing a stick "bent" if one half is underwater, leads to misinterpretations, it is due to our misarable ability of sensing the world as it is. This is what makes us finite.
You have to keep in mind the main point of transcendental idealism: We have to say there is a reality out there, but we cannot possibly say what it really is like. There is a logical necessity so say there is a reality destinct from our mind, but we can only know what we can make out of it, therefore we have to be agnostic about its nature (possible, highly problematic exception: the moral law). See regarding the reality of things in themselves and our knowledge e.g. this question
As an aside, Kant later formulates that this correspondence between sensibility and understanding is felt as beauty (§59 Critique of the Power of Judgement).
The influence of our "transcendental" subjectivity on objective reality is, according to Kant, a matter of enforcing apriori rules, and only apriori rules. Whatever is not knowable apriori is, then, open to ordinary error.
What we dictate to objective reality is arithmetic, geometry (our mathematics), and the principles of the categories, which are meta- laws of our physics (law of conservation, law of causality, law of mutual action).
Everything else about objective reality, everything that is not knowable apriori, is not dictated by us, but by the things themselves (duely filtered by having to comply with our apriori subjective conditions). These data - the a posteriori - are knowable through the senses, in combination with judgements of the Understanding. But the senses might lead us astray, and our judgments may be negligent and wrong. This part is not different for Kant than for a realist. It is untouched by the idealist aspect of Kant's metaphysical view, which concerns, again, only features of reality that are knowable aprioi.
Except for in the case of thetic judgements, all judgments are synthetic in nature, requiring a unity between a subject and a predicate. A similar unity is also required for thetic judgments, because Kant regarded them as involving the relation between an object and a concept (Critique of Pure Reason, A599/B627). Because of this, Kant's theory of truth is based on the conditions under which such unity may be brought about:
"[I]t is the unity of consciousness alone that constitutes the possibility of representations relating to an object, and therefore of their objective validity, and of their becoming cognitions, and consequently, the possibility of the existence of the understanding itself." (Critique of Pure Reason, B137)
Consequently, he makes a distinction between subjective validity and objective validity. Objective validity only occurs when objects can be brought under the objective unity of consciousness, which, in turn, involves being brought under the conditions of judgment. According to Kant, these are summed up in the categories. The following is a good illustration of his distinction between subjective validity and objective validity:
"In this way alone [i.e. being brought under the objective unity of consciousness,] can there arise from this relation a judgement, that is, a relation which has objective validity, and is perfectly distinct from that relation of the very same representations which has only subjective validity—a relation, to wit, which is produced according to laws of association. According to these laws, I could only say: 'When I hold in my hand or carry a body, I feel an impression of weight'; but I could not say: 'It, the body, is heavy'; for this is tantamount to saying both these representations are conjoined in the object, that is, without distinction as to the condition of the subject, and do not merely stand together in my perception, however frequently the perceptive act may be repeated." (Critique of Pure Reason, B140)
Without the conditions of objective validity, we can associate one feeling with another as we experience the world, but mere association is not the same as attributing those impressions to an object. Such an association only gives subjective validity to our experience. On the other hand, objective validity involves that our experience of reality is objectively determined. It is only under such conditions that properties are conjoined to the objects to which they are attributed. Without the synthesis which unites a subject to a predicate, we lack the necessary conditions for asserting that our judgments are true.
Since judgement is a spontaneous act of the understanding, error arises in the misapplication or lack of application of judgement. Kant addresses the subject of error as follows:
"It is [...] quite correct to say that the senses do not err, not because they always judge correctly, but because they do not judge at all. Hence truth and error, consequently also, illusory appearance as the cause of error, are only to be found in a judgement, that is, in the relation of an object to our understanding. In a cognition which completely harmonizes with the laws of the understanding, no error can exist. In a representation of the senses—as not containing any judgement—there is also no error." (Critique of Pure Reason, A292/B348)
Furthermore, the distinction must be maintained between the subjective and objective determinations in order to avoid error:
"But, as we have no source of cognition besides these two [i.e. sensibility and the understanding], it follows that error is caused solely by the unobserved influence of the sensibility upon the understanding. And thus it happens that the subjective grounds of a judgement and are confounded with the objective, and cause them to deviate from their proper determination, just as a body in motion would always of itself proceed in a straight line, but if another impetus gives to it a different direction, it will then start off into a curvilinear line of motion." (Critique of Pure Reason, A292/B348)
One way in which an unobserved influence of the sensibility can adversely affect our judgment is by means of the imagination which "has only subjective validity" (Critique of Pure Reason, B140). Kant asserts that the imagination has the crucial role of providing the synthesis of what is provided by the senses, but such synthesis is not enough in itself to form objective cognitions:
"Synthesis, generally speaking, is, as we shall afterwards see, the mere operation of the imagination—a blind but indispensable function of the soul, without which we should have no cognition whatever, but of the working of which we are seldom even conscious." (Critique of Pure Reason, A77/B102)
Kant points out that there are two main categories of error: "empirical illusory appearances" and "transcendental illusory appearances." The former includes errors such as optical illusion in which we are misled by the imagination (Critique of Pure Reason, A292/B348); and the latter are those that may lead to the philosophical errors of which he treats in the Transcendental Dialectic. In either case, Kant makes it clear that error is ultimately a question of poor judgement in distinguishing the subjective influences from the objective:
"Hence truth and error, consequently also, illusory appearance as the cause of error, are only to be found in a judgement, that is, in the relation of an object to our understanding." (Critique of Pure Reason, A292/B348)
"Transcendental dialectic will therefore content itself with exposing the illusory appearance in transcendental judgements, and guarding us against it; but to make it, as in the case of logical illusion, entirely disappear and cease to be illusion is utterly beyond its power." (Critique of Pure Reason, A296/B352)