Hm, some thoughts:
The male-only draft (in countries that have one)
While not exactly fair, I don't see that as that bad (I got drafted, I might add). Assuming a draft is necessary in principle, I don't have the feeling it would be better if everyone had to go there. It doesn't really help me if others have to lose time there as well, does it?
If you select a certain percentage out of a age group for the military, some will always be unlucky. Assuming I support a draft in principle (not saying that I do or that I don't), I can't really complain that one of those unlucky to be drafted is me.
Don't really see that as sexism, only as lack of concern for bodily autonomy that happens to be more relevant to men in the USA. In other countries it's more relevant for women. I.e. just a "human" problem, but one that we should still solve.
Cavalier attitudes toward men's pain and sickness, AKA "Walk it off!" The Success Myth, which defines a man's desirability by his material success. Also The Myth of Men Not Being Hot, which denies that men can be sexually attractive as male beings.
I think those describe a problem that many men feel. That there's a huge pressure to have power and control. Sickness or visible showing of pain means a lack of control, so that's bad. On the other hand, I believe many men LIKE it that way. At least in western cultures.
Sexual abuse of men
A problem for everyone, so I don't really see it as "Men's issue"
That's the ONLY point that really bothers me on the list (as a "Men's Issue" ). And one that is fortunately changing here (in Germany). The fathers position was continously strengthened over the last 20 years, first giving shared custody after divorce (instead of just giving the mother custody), and after a recent ruling of the supreme court fathers gain shared custody at birth, even if father and mother weren't married or lived together. I don't know the situation in the USA though.
General attitudes that men are dangerous or untrustworthy.
Not a problem that I ever had personally, I think it's not that important in social interaction (at least here - I don't know the situation in the USA), and more important for the possibility that you get caught in the justice system while innocent.