I actually had a pet adoption totally glitch out once: The agent walked in alright, but just kept putting down the pet carriers until there was no more space in the living room - with no pet in sight. While that craziness was going on I actually did find the cat my sim was trying to adopt somewhere way off the lot. I thought, no problem just make nice with the kitty and adopt him and then end the process. Well, I adopted the pet, renamed him, paid the fee and ended the process because my sim wanted his living room back. But the agent still took the pet with him. I was really bummed. Fortunately when I tried to adopt the next day, that cat was still among the choices with the new name I had given him!
I think the adoption glitched out because I had the front door looked for everyone but household members, because I never had that issue again.