Trying to curb unwanted behaviors

Question
We adopted a 1 year old Bulldog/Pit mix in February. He is potty & crate trained and a very good companion. Within the last couple of weeks he has started urinating &/or defecating on the carpet in various spots--often right after he was let in from outside (where he is supposed to go).  It would be nice to have him be an inside dog (except to potty & some play time), but this new habit makes it tough.  Any ideas would be greatly appreciated.

Answer
If this behavior is sudden, there are a couple of possibilities.  First, is he neutered?  If not, this could be marking behavior that can emerge as the dog reaches social maturity.  Has he been checked by the vet to rule out any physical causes?  Also, have there been any changes in your family?  Have you moved, divorced, had a baby, etc.?  Other possibility is that he wasn't as well house trained as you thought.  The solution for that is to start from scratch and re-train him, being careful to supervise him whenever he is out of his crate.