While YOU may think that you are a "good person", even good people who have never committed a crime and have always behaved with integrity are not all qualified or suited to be a police officer.
Simply wanting to be a cop is not enough. Your candor about accepting your fate is commendable, but at the same time you attempt to minimize your past by using terms like "mishap" and "mistake"
You didn't make a mistake unless you meant to sell vacuum cleaners but the box had drugs in it when you sold it.
RO56 had good advice also, I'll just say that LE is just not a career choice for you.
Stay straight, get an education, and try to help your fellow man. Life is as rewarding as you make it. ;)
"Speed is fine, but accuracy is final" --Bill Jordan
Remember those who died, remember those who killed them.