What are the problems of having a tooth taken out?

A few. If i understood your question well: 1. Extracting a tooth is losing a tooth and depending on its location it causes esthetic or functional problems. Functional is not being able to chew well. 2. When you lose opposing or adjacent tooth other teeth can shift and move due to lack of contact. 3. Extracting a tooth vs saving it with root canal if later you want to place implant is more costly sometim.
Tooth loss. If you do not replace extracted tooth it may lead to loose adjacent teeth. Also it can cause a bone loss.