If a dentist is on any/final warning, does a patient have a legal right to this information before receiving treatment from him?

Usually it is a 2/1/2 year Statute of limitation here in New York. Do you mean warning from the State Health Dept? More likely you mean from the employer. Even if you were not told about it in advance, IT CERTAINLY ENHANCES YOUR CLAIM AGAINST THE EMPLOYER, as well as the dentist. Get to someone Right away. Best wishes.
Bob Brenna Jr.
Brenna@brennalaw.com
Brenna Brenna And Boyce PLLC
Rochester, New York 14625