The first question you may want to ask is; will I have some kind of a schedule?
Many (Not all) corporate pilots are "On call" 24 / 7/ 365.
It is important that you find out what, if any, your scheduled "hard'' days off will be. A "hard" day off being one where you know ahead of time that you will not be called versus a day where you are at home but still on call and have to be available.
Fortunately most quality flight departments schedule their flights well ahead of time and have very few "pop up" trips. Some departments only work Mon. to Fri.
There is a great deal of variation with how companies handle schedules, and coming from the airlines, I think you may find this to be one of the biggest differences.
Next question you may want to ask is what if any kind of flight time / duty limits do you have. In the USA, corporate flight depts. usually operate under part 91 of the regulations and as such there are no limitations.
Most corporate departments have very good maintenance, but you may want to check on the reputation that your intended employer has.
Once you have those questions answered you can then move on to trivial questions like salary etc.
Just re-read the second part of your question.
I guess I already answered one of the negative aspects of the job in my previous post (Schedule)
For me, one of the positive aspects is variety, I don\'t think you can beat this at an airline job. Some trips may involve a weeks layover at some exotic beach resort and some companies even let you bring your spouse along. (Of course, you may not want to)
I also enjoy the interaction that you have with your passengers, many times the people that I fly turn a trip into a paid vacation with friends. That said, you could end up working for an a**hole, which is no fun, another reason to ask around about a potential employer.