I've had six dogs and can confidently say that, while I don't think you can directly diagnose dogs with human ailments, they certainly can have their own mental issues that are similar to some we experience.
One, which was a stray we took in and ended up keeping as the owner was some ~20 year old cokehead who didn't bother to feed it and her mother said she couldn't handle the responsibility, has clearly been shaped by the experience. While he's lived with us for 12 years he, to this day, is an aggressive scavenger, is extremely crafty and intelligent (makes my other dogs look like dunces), is always trying to sneak out of the house to wander the neighborhood for a while, and most of all has an extreme separation anxiety unlike anything I've seen.
He'll practically trip you up as you walk as he's trying to make sure to be close enough that you won't have time to close a door between yourself and him, and he'll start barking and scratching like mad if he finds himself alone. Basically, he becomes a dang lunatic when separated.
The other dog with issues has always, from the time he was a puppy, being very unusual in all things social... he would shake without cause, snap at you if you picked him up in a certain way (there was nothing the vets could find to suggest injury), would look for attention on occasion but you could only pet him in a very specific way or he'd freak out and run... My mother worked with special needs kids and said she'd observed many varieties of these behavior, so it seems to me that he probably has SOMETHING going on there.
So yeah, in 2/6 instances I've definitely seen clear signs that the dog is dealing with mental issues that would normally get diagnosed in humans.








