All the animations in 2002 are supported in 2007.  There should not be any
problems, so if there are, I would suggest some basics.

1) Make sure all the Office and Window updates are applied.
2) Make sure DirectX is current and up to date
3) Make sure the printer driver is up to date (don't ask, you'll be happier)
4) Deactivate virus scanning (only if not connected at the time)

Then, if the problems do not go away, I would try to localize them.  What
animations? When?

I am not a ppt 2007 user, however, I did experience some animation
difficulties when using a ppt 97 presentation in ppt 2003. I discovered that
the culprit to my difficulties was that 2003 wanted to apply an animation
scheme to my slides. The animation scheme over-rode my slide specific
animations, and the transitions between slides.

I would recommend checking if ppt 2007 is applying an animation scheme.
I would also check if  the slide masters have acquired animation /transition
settings for the slide and placeholders that could be altering your animation
settings.