I've been seeing a recurring situation where non-Mastermind pets have trouble following a toon through a doorway. I first noticed it with a Controller's persistent phantom pet. It would get stuck at a door that the toon would use, such as entering a store or City Hall. The pet would remain there "bouncing" around as if trying to navigate through the door until my toon zoned. Then it would respawn in the new zone.
I also saw it in a door mission, rescuing Ice Mistral. She becomes a pet, but she couldn't follow through an Oranbega teleport doorway. She became stuck at the gateway, wouldn't reacquire a toon as the Follow target.
I have not noticed this with escort missions, though.
Fyi, I did submit a support item about this, #40828. I wanted to log it here though, since I did see the problem in a mission recently (the Ice Mistral glitch).