It seems like TYT is objecting more to the hypocrisy of being pro-vietnam when it was going on but not actually doing anything about it than the fact he dodged the draft.
There are plenty of legitimate reasons why people would dodge the draft that don't make them bad people. But his reasons are a bit weak. He's saying 'Oh I wanted to go, but my hands were tied' Basically, he's lying about what he really thought about the war. I think if he'd just said 'yeah, i didn't want to go to war' then TYT wouldn't have attacked him on it because it's the truth. Of course, that would be political suicide among the voters.
but anyway, from looking at the news from the US, there seems to be plenty of reasons not to vote republican other than romney didn't want to go to vietnam. republicans seem crazy and almost clownish from here.