There's been a lot of chatter about Traveller over at RPGSite, which got me back into it a bit. I have owned every edition of the game, and played most of them. Mongoose is still my favorite.
In any case, I think the Third Imperium was just awful. There was no frontier, and no really evil enemy that military-based campaigns could just go off and blast with no issues (the Zhodani were sorta-Russians, but basically just the Imperium with psionics).
If there had been a completely open border, and a border with something like tyranids, I think the setting would have been dramatically better. Having an enemy who was only interested in eating you, with no chance of diplomacy, just makes a game more interesting to me.
In addition, the setting is very anti-psionics, which I think is just dumb. Psionics are cool. In most games, they are a generic version of the Force from Star Wars, and what kid didn't want that in his game.
The default 70s era technology hampered the game, and when the Virus was introduced to try to fix the setting, lots of players were pissed. I think GDW would have been better off just creating a new setting, but sadly, that didn't happen. I personally liked the New Era setting. Unfortunately, the rules were not nearly as good as Classic Traveller.