Are there a lot of things that can cause a denied medical? Can fairly routine procedures be grounds for denial? (Please don't hate me for having 2 questions in one!)
Its really no big secret, the FAA publishes their full guide for AME's and you can read it if you like (all 514 pages...) and generally speaking it lists a lot of the disqualifying factors. They offer various guides as well, all of which are public.
If you are worried that something relating to you personally is grounds for denial you can always reach out to an organization like AOPA for assistance.
Routine Procedure is a fairly broad term and an answer cant really be provided since this can be highly case by case depending on what the procedure is.