What kind of problems can an ill fitting bridge cause?

Your bridge should not be loose or not fitting correctly.  This can cause recurrent decay or unnecessary stress on the anchor teeth of the bridge resulting in loss of those teeth.  If you are not feeling comfortable with your result have another dentist give you a second opinion.  Hopefully, everything is fine.  Good luck.  

Your bridge could be loose because it just doesn't fit the prepared teeth or because your bite is loosening it. Either way, it should fit properly without gaps. If it continues to be loose, it can cause chipped, broken or decayed teeth over time.

You should have the bridge evaluated by a different dentist.  Bridges should not be loose.  Best to not wait on this as a lot of damage can happen if the bridge is truly loose.  Good luck!