Test scores that hover near room temperature are a start. If you have to take a civil service or any sort of entrance test, prepare yourself before you take the test. No, you will not be "miracled" through this, and doing average does not cut it. You are competing against others; every point counts. Study and prepare.
Bad oral interviews will derail the best of young candidates. Find a book to prep with or seek a seasoned officer and practice interviewing. Interviewing can be a nervous time; it can be overcome with practice. Watch what you say here.
When I was in Savannah, I chaired a candidates' interview board. We had a pat question: Why do you want to be a police officer? All we want to hear is that you want to help the community, are willing to work and you care…boiler plate stuff here. Oh no, this one sterling lad stated he was ready to give his life for the city. He worried us, a lot, and he did not get past us.
Double check your application. Errors and omissions on the application can mean an early exit from the process. If you put something on that application it had better be the gospel truth. If there is one falsehood or error, you are toast.
References are another issue altogether. A good background investigator will ask a reference to name two or three people who know you. These may not be the ones you want us talking to, so be sure of who you put down. Please tell your references that they may be getting a call. If by chance they do not want to be your reference this will be a warning light.