Users of mimetex, or of any gpl'ed program, should first agree to the terms and conditions of the gpl. But, at least in the United States, people under the age of 18 aren't legally competent to agree to anything.
Wrong. Varies from state to state, but there are certainly things minors are considered competant to agree to, for example educational loans and life insurance(!). Or contracts for necissities (e.g., food, shelter, clothing, medical care).
For example, suppose you sell a bicycle to a 15-year-old for $500, and he gives you $100 down and signs a contract agreeing to pay you $100/week for the next four weeks. Well, he can just ride off on the bike and forget you and your agreement. And you have no legal recourse -- no court will uphold the contract nor even order the kid to return your bike.
Wrong. Contracts with a minor a generally voidable, which would mean the minor would return the bike and you'd return the money (possibly minus any wear/damage on the bike).
A quick google search for contracts with minors yeilded many explanations of this concept, one with an example very similar to the above (a stereo, instead of a bike).
Returning to the gpl, the same 15-year-old could, for example, incorporate gpl'ed code into a proprietary product, and there'd be no legal recourse.
Wrong. The GPL isn't what stops me from using your code in a proprietary product. Copyright law does, and copyright law definitely applies to minors.
The GPL is what allows me to use your code in a GPL-compatibly licensed product.
He could even sue the author of a gpl'ed program for damages if the program misbehaves.
Correct. So could anyone else, however.
The author would probably win, but couldn't just use the gpl to get the case dismissed.
Yes, he could, at least to the same extent he could against an 18-yr-old.
It seems to me that the gpl fails to adequately address this kind of loophole -- that is, in order to agree to the terms of the gpl you must first be a legally competent person.
What you are missing is that the GPL is not a contract. It is a grant of non-exclusive copyright license.