With Scooby-Doo, obviously, because Scooby and Dynomutt shared a timeslot and the characters crossed over many times.
Also with Superfriends, because of their similar premises (lighthearted superhero entertainment) and the fact that Blue Falcon is a stand-in for Batman.
There was an episode in which some supervillain's Weird Science ray gun made Blue Falcon — who was a human being, not a robot — melt into a blue puddle. That Dynomutt restored him a couple of scenes later did not do much to mitigate the big whopping nausea-inducing dose of Body Horror, nor did the Laugh Track.
The one where the villain used TV signals to turn humans into blimps wasn't pretty, either. Especially when, after Blue Falcon figures out what's causing it, Dynomutt decides to see what the TV news says about it...
You're forgetting one where Dynomutt and Blue Falcon make their appearance in Dexter's Laboratory where while Dynomutt was talking to Blue Falcon about how he made sure the diamond was safe, the villain they were facing, Vultor I believe, stabbed Dynomutt right through him with his claws. Believe this troper that when the scene is replayed, it can be horrifying at most, despite the robot dog's falling with Vultor's claw holding the diamond being silhouetted.
Seeing the normally-lovable Dynomutt being turned into a vicious brute in the Cartoon Network motion comics is pretty shocking to a young psyche.