I would also ask how old the pump and filter are, look for signs of leaks around the pump/filter or around the pool itself, and let them show you the operation of all the valves/handles so there's no confusion when it's your job to take it over. The more information you can find out about the pool and its components, the better--and if you stay on good terms with them after the close of the house, it wouldn't hurt to have their phone number handy in case anything comes up that you need to ask them about.

Is the pool chlorine, or bacquacil??

Janet