What are some things that increase the chances of getting mouth cancer?

Several. Oral sex, has become a major cause, due to the hpv virus. Hpv has been spreading oral cancer much more rapidly than in years past. Multiple sex partners has been shown to expand the incidence of probability exponentially. Heavy smoking, heavy drinking and an unhealthy lifestyle are also contributors.
Oral cancer causes. The main causes of oral cancer are smoking, drinking excessive alcohol, chewing tobacco, and human papillovirus. Good clinical examinations are ways to catch things early.
Avoid these. The main causes of oral cancer are smoking, drinking excessive alcohol, chewing tobacco, and HPV. Frequency of cancer will increase with increasing frequency of exposing oral mucosa to these agents. See oral surgeon or ENT doc for early diagnosis.