My first suggestion is to not cancel our appointments if the dentist leaves the game. Instead, if the client is still in the waiting area, make it open for other dentists to claim as it is annoying to get kicked from the waiting area and repeat everything again.
Second suggestion is to let us see if our appointment has been claimed. I know it does let you know, but only for a short amount of time. It'd be better if there was a button that you could click to see if your appointment is claimed, who and when claimed it, what type of appointment it is, etc. Maybe even an appointment history (just for fun).