Noticed when I deleted some measures, dragged and dropped the midi tracks the exact amount to fill the whole from right to left, the notes' position weren't that exact. They missed the beat with almost 1/32. Anybody else experienced that?

Did you have auto snap on?

No I didn't.

Oh wait... sometimes your zoom level impacts the precision of things like this... like nodes in an envelope for example. If you zoom out and move the whole envelope, it may not move as precisely as if you zoom in first.
 
Try zooming in before moving the clip. I know, this shouldn't matter, but it might help you.

Try this: Go Edit > Preferences > Customization > Snap to Grid, uncheck everything under Landmarks, and see what happens. Sounds like you might be snapping to landmarks you don't intend to snap to, like clips. If one clip is off and you snap to it, the snapping will be off.

Thanks a lot Craig and gswitz! I'll try your tips as soon as I get home from work.