Hi George
I think it’s fair to say that any serious legal issue in an author’s past is going to be problematic, if you want to write for children or teenagers.  Obviously, it depends what the background check would reveal. A parking offence probably wouldn’t pose problems. But anything more serious is likely to deter both agents and editors due to the obvious sensitivities of working with young people. It would be very difficult to get published and for the publisher then to discover their author has a skeleton in the cupboard that could come to light later on and cause problems. 
I’m sorry to have to say this, but I think that’s the case. There might not be as much sensitivity to this for other readerships – for example, if you were writing non-fiction for adult readers.
Sarah