Well, unless they are carefully run and maintained you have an increased
risk of pest infestations and an increased risk of fire.  They should be
located well away from exhibit and collection storage areas, if possible.
Trash disposal should be carefully monitored.  There are also sometimes
problems with people trying to walk into exhibit areas directly from a
restaurant, especially one that is "fast food" style, with a soda or cookie
in their hands.
That said, some museums have well designed, well located, and well maintained
restaurants with GOOD food that is not overpriced.  These can really enhance
a visit for a tourist with a limited amount of time to see a museum (who does
not want to have to wander the neighborhood looking for some place to eat
after walking their feet off in the museum for hours!)  Staff like them too!