Yes, you can have some problems with dentures.

The first problem with having dentures is that, the mouth is not use to having in it other than food. With brain thinking that you have food in your
mouth but it's actually your dentures, you will produce more saliva. Luckily, this will only happen for the first twelve (12) to twenty-four (24)
hours, then the saliva glands will return back to normal.

Another problem with having dentures is if you have a new full upper dentures. Then you will loose the sense of taste.

Another problem with having dentures is gagging. This can be caused by different things. What can make you start gagging is the dentures might be extended to far on the soft palate or the dentures are too hard or too
soft. Gagging is the hardest problem that the dentist can fix. Since gagging is out the dentist control, a lot of times a dental implant is considered.
Something else that be causing the gagging is, there is gingivitis built up under the full set dentures.

Another problem with having dentures is sore spots. This is caused by the dentures putting a pressure of the mucous of the soft tissue. This can fixed
after a couple of dentist appointment after the insertion of the dentures.

Keeping them in place is very important. For your dentures do not fall out of your mouth and hit the floor and shatter. If that happens then you will have to sit though a whole new process.

The final problem with having dentures is keeping them in place.

There are three (3) rules for wearing removable dentures; retention, support and stability.