Not only does the Chief Caretaker have a Hitler moustache, the other Caretakers salute by doing a Hitler moustache impression. This is clearly a deliberately unsubtle way of indicating that they are obvious baddys, perhaps even a parody of the Daleks doing Nazi salutes during the Dalek Invasion of Earth.
Part two resumes with the Chief Caretaker sentencing the Doctor to death, but then he gets 'phoned to be told about the disappearance or death (we only hear his side of the 'phone conversation so we don't know which) of the Caretaker from part one. We know he knows about this already, but he has to go and investigate because it says so in the Caretaker rulebook. He leaves his deputy and one other Caretaker to guard the Doctor.
The Doctor is confused about why Caretakers would be attacked by Cleaners, but he works out that the Caretakers do whatever is in their rulebook so he tricks his guards by pretending there are rules in their rulebook to allow him to escape. This is a typical bit of Doctor cleverness and is a good scene.
There are several short scenes, almost a montage, of the Doctor and Mel and Pex in carrydoors looking for each other. The Doctor almost gets caught between two Cleaners but escapes them by accident when he falls into a hole in the wall. He ends up where the Red Kangs are.
The Doctor is starting to work out some of what is going on, and impresses the Red Kangs by making a vending machine work.
The Chief Caretaker goes to the NO ENTRY door. His pet lives behind the door and says
"HUNGRY!"a lot in a scary voice. Even the Chief Caretaker is scared of it, when he is trying to give it into trouble for getting itself noms that he did not send to it. This is some ominous foreshadowing of what will happen later on in the story and adds yet more mystery - if even the Chief Caretaker is not behind the actions of the Cleaners and his pet, who or what is?
Mel and Pex get captured by the Blue Kangs. They say Pex is a "scaredy cat". He is not a cat(!) but he was scared, and is ashamed that he ran away from a war. Pex says
"I've made up for it since I was here. Since I've been in Paradise Towers, I've been brave! A hero!"Scary Cat likes Pex. He knows that not everyone can be as brave and scary as he is, but he admires Pex for trying to be brave. Mel leaves Pex behind and, lost, goes straight back to Tilda and Tabby who still want to nom her.
The Caretakers come to raid the Red Kang's base, with a classic example of cutting through a door to get to them. Fire Escape thinks the Doctor has brought them here, but he pleads with them to believe him and to team up with him to fight the Caretakers.
With time rapidly running out, Tilda and Tabby decide to nom Mel to give us a cliffhanger ending to this episode.
Part two continues the good work from part one - even as the Doctor solves part of the riddle of Paradise Towers, more mystery is revealed to us viewers like layers of an onion. There is a certain amount of padding to this episode, and the ending feels a bit like a contractual obligation cliffhanger, but this is more than made up for by some solid scenes which mix comedic and dramatic moments well, and depth is added to the character of Pex.
Plus who doesn't like a bit of 'cutting through doors' action?