Signs to watch for include bubbles, excessive dripping or constant sneezing. Hedgehogs can get all manner of things caught in their mouths, especially in the roof of the mouth. Peanuts, as provided in the Vitakraft hedgehog food are probably the most infamous. Again, these can be deadly if not removed. This can sometimes be seen by a hedgehog licking its chops excessively, and not eating.
Some hedgehogs can also develop abscesses in their mouth.
This is most often indicated by a hedgehog eating on only one side, or avoiding hard food. This is definitely a case for a quick trip to the vet. Often these problems can be handled without complications, by a vet if caught early. Hedgehogs can also suffer from tumours and cancers of the mouth. These can be much harder to see, unless on the outside, and require prompt veterinary care, when detected.