Regarding the statement from your question:
"it isn't valid"
By definition, an argument is valid if the premises and our accepted working of logical rules create a situation such that if all of the premises are true, then the conclusion cannot be false. From the detail in your question I assume you are aware of this much.
Having redundant premises is not a problem. For example, I could make a simple argument:
I own a dog,
Today is Tuesday,
Therefore, I own a dog.
This is perfectly valid (albeit trivial), and from that point of view there is nothing wrong with it. Introducing a premise that has nothing to do with the conclusion is not a sign of invalidity, but may be a sign that the argument has been lazily constructed (if the author does not realise that it is unrelated), that the argument has a secondary function other than proving the conclusion (an anecdote may contain evidence to a conclusion, but also contain irrelevant information to be entertaining at the same time), or because they are trying to underhandedly overcomplicate things or insert concepts that have no relevance in order to make the conclusion more palatable (see: politicians).
None of this makes the argument invalid as far as logic goes. You could, however, make the point that because of this the person is arguing poorly (or at least sub-optimally), but the abstraction of language to logic and argumentation as we teach in philosophy classes is not one-to-one with the usage of language in real life.
How can I logically infer that something was redundant without using much brain power to figure out this kind of mistake?
The only way I can see of doing this would be to create a truth table/tree/etc. and then by brute force check to see which premises have no effect on the truth-value of the conclusion. Then if you find such a premise, you know that it is redundant (and sometimes this happens entirely innocently, but because one of the premises e.g. becomes part of a larger tautology of which several of the components are not needed).
P.S. This is just speculation, but I suspect that this problem arises because of the assumption that if someone includes a statement in their argument, then they must believe that the statement lends logical support to its conclusion. This could actually lead to an interesting discussion about whether when we make an argument we are also creating a second logical argument in tandem that asserts that the logic used in the original holds water, and that both of these 'sub-arguments' need to give a true conclusion for the 'argument' as a whole to be 'acceptable'. This would be why we can attack an argument by attacking it's use of logic instead of simply trying to disprove its premises, and the statement "Premise A is relevant to the conclusion", "Premise B is relevant to the conclusion", etc. might be implicit (or not) in that tandem argument.