While most of it isn’t a security concern, though it may be if you’re using Row Level Security, Dynamic Data Masking, or Encrypted Columns, you should try executing it as other users to make sure access is correct.
When I’m writing stored procedures for myself or for clients, here’s what I do.
Click through for Erik’s guidance. The premise is couched in security testing, though much of this is functionality and performance testing Regardless, it’s a good plan.