That's....really strange. I had none of these issues at 60fps. Hell I finished every single GTA that came to PC. Dunno what to tell you really.
If there is one thing about old GTAs that sucks, is absence of controller support. Back then I didn't care, but now I play my PC games on TV so it would be handy. Although...I am probably never going to replay them, so bah.
You won't always notice it but the game isn't running 100% correctly above the framerate of the framelimiter, i had plenty of playthroughs where i encountered few issues, others where...well i got the ones i specified.
Yeah, controller support not being there is weird, given that they have classic aiming / shooting in there which i believe is the default console lockon system.
Edit: The windows 8 version has 360pad support but not sure how good a version it is.