What are the problems after oral cancer surgery?

Yes. Most problematic is the lack of saliva. This amazing juice has countless functions including lubrication, digestive enzymes, antibacterial proteins and as yet unknown properties. Your ENT dr has some helpful ideas.
Many possible. A major one is the affect on your saliva flow. Surgery, radiation or chemo can cause drastic changes. This can cause you to become rapidly susceptible to many cavity changes. Work with your dentist to evaluate this as well as to increase the preventive aspect of your routine care. There are many other implications as well.
Extent of tumor... The problems that follow oral cancer surgery are like other cancer surgeries. In this case it really depends on the siz, location and type of tumor. The affected structures is what would cause your troubles. Be it a tongue, tooth structures, glands, muscles etc. The mouth really does work well with all its pieces but we manage to do quite well when some are missing or damaged.