My 13 year old dog has arthritis and sometimes has accidents in the house. This is very out of character and she shows no remorse. The accidents are faecal and look slimy. Is this a symptom of something.

She could be losing touch with her back end. The vet might or might not be able to give her a few more good years. It certainly is worth an office visit to find out.

Dogs don't show remorse. It is a me, me, me world to them. They aren't capable of feeling guilt over something. I agree with labman. She may be losing her ability to control her bowels, or she could have picked up an intestinal parasite that is making it tough for her to hold out until you walk her. Time to go back to the vet and see if they can assess what is going on. Scoop up a sample for the office to test. If they can first rule out any parasites, viruses,. they then can focus on the physical aspects.