I noticed today that underscores are not allowed in the argument of the question environment.

This took some sleuthing and quite a bit of guesswork. When writing the test (24 questions long with several groups of questions), I had no compilation errors. It was only when preparing the test in the AMC GUI that I got many missing $ inserted errors. Because of the way AMC wraps around the original file, the errors don't show up until the last line of the \onecopy{n}{} macro. So it was only through commenting out massive portions of the test, re-preparing, and so on that I pinpointed the problem. After changing undescores to hyphens the problems went away.

I am guessing that in the preparation the question IDs are scanned as regular text. But special characters like _ are useful to "namespace" IDs of questions that come from a similar bank. So I'm wondering, in whatever TeX process that's scanning question IDs, can the category code of _ be changed to make it a letter?