^I'm so glad that this attitude is slowly starting to disappear. Aquaman is a great character that has gotten a bad rap for a few less-than-flattering portrayals. The New 52, Injustice, Flashpoint Paradox, and other recent media have been doing a fantastic job of re-imaging the character and starting to help some people (including myself) take him more seriously.
Let me just say that I feel like the Damon rumors are pure speculation that started from that joke of "if Ben Affleck is Batman, they'd better make Matt Damon Robin". There is no way that WB is casting any expanded universe roles yet since they've proven to be following a movie by movie development plan. All eyes are on Superman/Batman right now, and if any role searching is going on, it's probably for a cameo capacity which may not even include the actual actor/actress to be cast in any role (see Thanos in Avengers).
Of the three characters here, I guess Aquaman would be the most interesting choice to place him. I can see him as Flash depending on which one we're talking about, but certainly not Martian Manhunter. Matt Damon isn't stoic enough for that, he'd probably be playing a completely new direction of the character if cast for it at all. But I'm betting WB isn't even looking at him yet.