Pool service is frequently taken for granted at the peril of pool owners. Owners can mistake it for a simple janitorial type function, equivalent to hire someone to mow the lawn. It is, however, much different.
A swimming pool is a body of water that you and your family will be immersing yourselves in and swallowing small quantities of. It is also the home of thousands of dollars of surfaces and equipment. Improper water chemistry can create unsafe water conditions, and jeopardize your equipment and surfaces.
May pool service guys are not much more than janitors, with little if any knowledge of pool chemistry. Ask some simple questions, such as:
What chemical levels do you monitor?
The answer should be chlorine, pH, alkalinity, calcium hardness, stabilizer/cyanuric acid, and (for salt pools only) salt. If he responds with anything less, he's not your guy.
What happens if the pH goes off?
The answer should be that if it goes to low, the acidic environment can eat away your surface, and that if it goes to high, it can cause deposits to accumulate on your surface which are difficult to remove, and your chlorine will become highly inefective.
If you get good answers on these questions, then you are dealing with someone who knows more than average, and you are off to a good start. From there, your questions should go to consistency of service, what to do if you are unhappy, repair capabilities, etc.