Very few things are insurmountable, with the exception of a most felonies and a very small number of misdemeanors. With that said, this is a very bad economy that means many people who are good candidates are now applying for police work who would normally not apply. That can be read as more time is going to be needed to get on with a good agency. If you are serious about getting on with an agency more quickly you might have to go with a lesser known, respected, or paying agency first. The best applicants will be hired by the better agencies while the not as good will be hired by the lesser agencies.
I would still apply at any agency that is hiring, because all hiring is done on a curve. You might be the best candidate at the time or the agency might overlook your transgressions. I worked for one agency that hired a guy who had something like 10 traffic tickets within the last 5 years and a drunk/disorderly within the same time period. Several other agencies wouldn't even talk to him until his issues were a few more years old. He turned out to be a very good officer.
But when a long train of abuses and usurpations, pursuing invariably the same object, evinces a design to reduce them under absolute Despotism, it is their right, it is their duty, to throw off such Government, and to provide new guards for their future security.
Translation for the intellectually challenged: If the government screws the people too much, it is the right and duty of the people to revolt and form a new government.