or (the following does not seem to be well documented, but appears to work)

  $$ dispalyed math equation $$

Hm, I have to admit I find this statement very surprising. It is extremely well documented in the TeXbook: 

I guess this might be the difference: That this is the way to do it in TeX, but not in LaTeX. Anyway...

I don't think there is any difference between equation* and displaymath but I could be wrong...

Well, I guess the question here would be, if you redefine one of the two, does that redefine the other as well? I dunno, I'm afraid I don't have a very deep knowledge of LaTeX either.

I think for purposes of scoping in TextMate we ought to treat them all the same.

I agree.

Upon further investigation of my file, the problem seems to be that all this falls also under the scope of meta.function.with-arg.tex, since it happens within the scope of a \comment{ command. If I close this command before the displaymath part, then it works fine. So this is not a problem simply to do with the math scopes.