Do PSP games look good on the Vita? Any weird stretching or graphical problems?
Also, is the 2nd thumb stick usable?
Yes.
2D sprite games look absolutely fantastic. I have these 2D games installed on my Vita: FFIV Complete Collection, Half Minute Hero, Sega Genesis Collection, Final Fantasy Tactics, ClaDUN: This is an RPG, Castlevania: SOTN, Alundra, Chrono Trigger, Final Fantasy V, Final Fantasy VI, and Legend of Mana.
They all look amazing on the Vita screen.
As far as 3D PSP games, well, they look pretty awesome as well. There is some jagginess, but the filtering option helps a little. Games that I have installed on my Vita that look really good:
Monster Hunter Freedom Unite, Gods Eater Burst, Chrono Cross, Final Fantasy IX, Vagrant Story.
Games that I used to have installed that look really good: Gladiator Begins, Final Fantasy Dissidia 012 Duodecem, The Third Birthday, Powerstone Collection, and Ys Seven.
Playing PS1 and PSP games on the Vita is like playing them fresh. Especially games like Dissidia, Monster Hunter, and Gods Eater, where you can map the camera to the right analog stick. It just feels so incredibly good. I can't imagine ever playing those games on a PSP ever again. Which makes it so frustrating that some games like Final Fantasy VII: Crisis Core, are unavailable on the PSN.
EDIT: I'm a 50ppp peasant, so top of page suggestion: Buy TEARAWAY! Fantastic game. I bought it full price, and don't regret it one bit!