There is some standard screening that occurs for people entering the military, plus whatever security clearance is required.

As long as it doesn't rise to the felonious level, or ridiculous numbers of tickets it should not be a problem. However...since it is competitive you might be at a disadvantage against another applicant with a cleaner record.

The military also does not care about FAA violations, unless it was criminal in nature (ie substance abuse).

Unlike the airlines, the military is not really hiring you for your skills, abilities, and judgement...they are hiring raw material which they will re-manufacture to suit their needs. They just want to make sure the raw material is adequate...