I noticed some bugs and glitches after only a couple hours of play. Sometimes when I try to get on a motorcycle, I'm mysteriously warped to a spot a few steps away. Also, under the pause menu, my statistics screen is filled with glitches; stats like popping a wheelie on a motorcycle, how far I've thrown people, how long I've driven on the wrong side of the road without colliding with something, etc. are all a little wonky. Fortunately, you DO still get Respect points for doing all these things, but your stats screen doesn't accurately keep track of everything you do.
And your homies are still very stupid: they'll sometimes shoot at cops on their own (kinda sucks when you're trying to keep a low profile), and they still don't understand that they can go AROUND obstacles. And they also can't jump as high as you, so some obstacles that YOU can climb over present impossible barriers for THEM. Sometimes the homies are more trouble than they're worth.
Hope this helps. Will update this post when I find more bugs...
 Yeah, the outfits thing. When I load up a save, sometimes my character's outfit is all messed up. For example, I saved a game with my character wearing a slick suit, but the next time I turned on the game he was wearing a T-shirt. WHAT???
I haven't had freezing problems (yet) but sometimes the GPS goes wonky too.
Yes, there are glitches all over the place. There are two main bad things about this game... one is the glitches... the other is how the cars appear and disappear so easily (even if they're right next to you). Those are my probs with the game anyway.
The customization is awesome... it's too bad that it has glitches too. For example, I go to save outfits, but they don't save/load properly.
Another problem I encounter is that you can be knocked INTO someone's car, going right through the roof (no collision detection) and they drive away with you upside down, or standing in the back seat. That kind of sucks when you're trying to complete a mission. That's happened at least a handful of times. One time, I got into a car in which a woman was standing THROUGH the engine and hood and I drove away with her stuck in it, and she was screaming in pain but she wouldn't "drop" out of the car.
lol. One time, my homie killed a pedestrian (all on his own, mind you), and the dead person's body was somehow stuck in my car's trunk, and as I drove away the woman's arm was sticking out through the back of the car. It was flapping in the air like a flag or something. Hilarious!
I've realized that it DOES accurately keep track of everything. It does so, whether or not you've saved the game on the same file, or haven't. You may not have saved doing these things, or you may not remember when you did, or may have done so on a different save file, but all of the stats are 100% accurate.
For example, I've only been arrested once, but I didn't save the time I was, and yet, it still shows up on the stats screen (I hate that it does). I also have two save files, one with a guy and one with a girl, and I've only played Zombie Uprising on the girl's save file, and yet, on the guy's, it still says I've killed 1300 zombies.
So, the stats are all inclusive, no matter what file you're playing on, or whether or not you've saved things.
There are a few glitches in the gameplay, yes. I know some people get P.O.'ed about it, but I don't really blame anyone. It's not like the game developers left them in there on purpose or even knew about them. I've been playing games for over 20 years, since I could first walk, and I've yet to come ANY game ever released to be 100% glitch free.
There are three notable glitches in this game, but none of them are really so big that they should stop you from playing the game.
The big one are the cars disapearing so quickly. In SR1, they did this, but cars didn't vanish as quickly as they do in this game. And because they didn't, we often got the problem of your car disapearing while driving and you being stuck in it, in midair. This happened most oftenly on the highway and in downtown. Mostly because there were too many cars/people on screen, at once. So they tried to fix this in SR2 but having less cars and people on screen at once, and thus, when any car isn't on screen, they vanish. This is really only problematic in two scenarios. One, being you're trying to collect a car for Chop Shop. They typically won't vanish as quickly if it's a car you have on your HUD, as their view on the map will keep them around a bit longer. The other problem is when you see a rare car that you like, like a Bezier, and you want to try to steal it. It can be a little annoying, but it's not like the game knows you want it. Yeah, I agree it's a small issue, but it really shouldn't bother you, too much, outside of these two scenarios.
The second "glitch" comes with the game occasionally freezing. It's a problem sometimes, and I think it has to do with the upgrade that comes with the game when you first put it into your 360 and play it. My solution would be to save every 10 to 15 minutes. They also have the Autosave feature to help you out with that, too. Yeah, the freezing sucks, but it's not like anyone making the game wanted it to do this.
The third "glitch" comes from the game's overall physics. But this isn't really a glitch as it is just how the game's engine works. Many people don't like it, compared to the somewhat-realistic walking and stairs mechanics of GTA IV. However, without this, we wouldn't be able to have nearly as much fun with the game. This engine system was done purposely, so you could have more fun with the game and do more wild and crazy things. However, I will have to admit that the whole ragdoll physics of your character and everyone else can be annoying, especially when a cop or enemy gang member tries to run you down on the street and you go flying up into the air, or caught betwen their car's wheels on the ground and end up being skidded to death. Sometimes, your character can trip over a bit of debris or wreckage, and really look like they've hurt themselves. That was the same thing as in the first game, so I've just come to live with it by now.
Everything else outside of these three things however, aren't really glitches and were intentionally put into the game. Some people don't like the driving mechanics after playing GTA IV's insane driving, but it's not a glitch. Also not a glitch is the "warping" feature that sometimes happen with people getting out/in cars instantly. Without it, your character could easily get stuck in their car when three police cars have you trapped in a corner and you can't open your door and your car starts to catch on fire. If it wasn't for that 'car warp,' your character would be trapped and left to die in that burning car. The same applies when you get stuck somewhere and the game warps you out of it and onto a safe spot.
So, these are the major three glitches in the game. None of them are really so big that they should stop you from enjoying the game, itself. The game is very well developed and no one's perfect. So, just be wary of these things and try to enjoy the game, despite them, because the game is still very fun!