Yes, Kant did consider Newtonian mechanics (or rather his variation on it) to be synthetic a priori in the same way he considered Euclidean geometry so, he gives detailed a priori "derivation" of it in Metaphysical Foundations of Natural Science (1786), see summary by SEP. The derivation of the third law for example goes something like this: changes of matter are changes of motion, changes of motion are reciprocal and equal by geometry and kinematics, every change has an external cause (the law of causality), so the cause of the change of motion of one body entails an equal and opposite cause of a change of motion of the other. "Newtonian mechanics" however only covered Newton's three structural laws, not the inverse square law for gravity, which was typed as empirical. Kant came close to declaring it a priori however, the only empirical input he thought it needed was the dimension of space, he gives an a priori derivation of it assuming that dimension is 3, which is similar to the usual modern explanation for matter fields with a point source and goes back to before Newton, see Who was first to explain intuitively the inverse square law of gravity? For detailed analysis of Kant's arguments see Friedman's Kant and Exact Sciences.
A blunder it was not, at least no more so than the whole idea of synthetic a priori as absolutes. Taking them as evolutionary and early developmental instead we can say that he most likely was right on geometry, and close to right on mechanics. Our sensory-motor stereotypes acquired in early childhood most likely hard wire something close to (at least locally) Euclidean notion of space, and some cross between Aristotelian and Newtonian notions of motion and force. This is why relativistic and especially quantum notions are so hard to process for most people, they require complete re-wiring of ingrained mental templates. See Brook's Kant and the Mind for modern perspective.
Kant certainly did not think that "the world" behaves according to connections in our minds. In fact, he thought that we can never know how it behaves or what it is, nor does science have anything to do with that. It is instead the study of appearances, of how things appear to us, not how they are in themselves, and it makes perfect sense that how they appear to us depends among other things on our mental constitution, including framing intuitions of space and time, and a priori categories of understanding that serve as templates for forming empirical categories. And to the extent that science relies on those bits it is indeed indubitable according to Kant. But that indubitability is very narrow and extends to mathematics and mathematical physics only, he explicitly excluded "purely" empirical disciplines, e.g. he classified chemistry as "systematic art or experimental doctrine but not a proper science", and declared that empirical psychology can never become even that.
Kant got some of the specifics wrong, mostly due to limitations of science of his time, and to the idea that the a priori are absolute, i.e. universal and unchangeable, was an even bigger misjudgement, but it is easy to say so only in hindsight. For his time he was a prophet, in big picture the modern understanding of our mental faculties and their influence on the formation and structure of science largely developed from the Kantian scheme, see What is Kant's influence on philosophy of science and the demarcation problem?
For post-Kantian notion of synthetic a priori see What are the more complex/interesting examples of synthetic a priori statements?
