Thank you for your interest in protective services! I served on the police applicant review board for a few years. I was a regular patrol officer. The rest of the board were ranking officers: a Sgt, a Lt, and some others.
The initial screening is looking for a person of good character: one who does not associate with persons of ill repute, has a good attendance record at school and work, does not steal from the employer., pays their bills on time, is not swimming in debt, has good relations with their neighbors/peers/boyfriend/girlfriend, etc, is honest, etc. Also one capable of physical work and teamwork - sports background helps, as does military/rotc.
On the Board, we looked for a variety of things. One would be self-confidence. When you, as an officer, are trying to tell an attorney he can't park where he wants to, he/she will spout law at you and try to tell you that you are wrong. You also need to have an understanding of the law, and all its nuances (it is illegal to do "xyz" except in case "a" or Case "b" if also "case c" applies.) You need to be able to articulate pretty well to get your point across. You need to be able to write a good report, explaining what occurred in chronological sequence. You need to be willing to take orders, and act on them promptly, even from people younger than you or people you don't get along with.
Different departments look at different things. But that is kind of a general overview. Hope this helps!