Signs of a mental handicap in a dog include an inability to learn commands, struggling with potty training, unnecessary and extreme fear, and socially awkward behavior. These signs normally occur early on in the dog's development.
According to Critters 360, Mentally handicapped dogs will often exhibit signs similar to some children with autism. In social settings, they will often behave at one of the extreme ends of the scale — either being overly friendly with new dogs and people or overly shy. They will often be overwhelmed by too much noise or commotion going on around them and will have trouble processing too much at once. The best thing for a dog with mental challenges is to keep it in an environment that has little stimuli and to keep it in a routine. Abrupt changes to the dog's usual routine can bring about extreme stress because it is too much for it to process all at once.
Dogs can also have other types of mental issues as well. These issues are almost the same as ones humans experience including obsessive-compulsive disorder, anxiety disorders, aggression issues, phobias and depression. All can be treated with either a very low dose medication similar to what is prescribed for humans with these issues or behavioral therapy.