Do apparitions ever appear to regular folks who have to go to confession more often than not, due to mortal sin?  

Or, does God only see fit to appear to near-blemishless individuals?

It does appear to be more often than not people who are already saintly who see apparitions (at least, of the ones that have been approved by the Church or that have any real credibility). Still, the conversion of the atheist Jєω Alphonse Ratisbonne upon seeing a vision of the Blessed Virgin in a church at Rome may be one of the most famous exceptions to this general rule.

I'm sure there are others, I just can't think of any off the top of my head.

Edit: Oh yeah, I guess I should add St. Paul, the spiritual 'predecessor' of Fr. Ratisbonne, if you will. Difference being that Saul wasn't an atheist, but rather a zealous follower of the Jєωιѕн religion, such as it was.