Okay, this is a Doctor Who story I can get behind. It is complete, it doesn't make my brain hurt trying to keep track of everything, and it all makes sense.
"Time Heist" was what I was hoping for: a caper with a twist. If we look at it in the right order, the Doctor and Clara get a phone call from Ms. Karabraxos, an old lady who was the richest person in the world, but she is now dying with one regret: that she took the last two creatures of a species, imprisoned one of them, and made the other act as security for her bank. When a solar storm destroyed the bank, she thought the species was extinct.
Her request to the Doctor was to penetrate the bank and save the species. The Doctor took Clara, gathered two other people - Psi and Saibra - that would be able to help (with the promise of being paid at the end), constructed a plan, and then wiped all their memories, so that they would have no trace of guilt as they entered the bank - which is what the species ("The Teller") detects.
The four of them enter the bank, find a bomb that scatters debris elsewhere and then reconstructs the area blown, enter the channels of the bank, find instructions to open the vault, almost lose Psi and Saibra, discover them again, and find the private vault which contains many riches and a much younger Ms. Karabraxos. She is still conceited and smug and leaves them to die when the solar storm threatens the bank, but not before the Doctor gives her his TARDIS number and a mention that he's a time traveler. Meanwhile, the Doctor finds the imprisoned companion of the Teller, and gets the six of them out before the bank is destroyed. They all go their merry way, except for Ms. Karabraxos, who eventually regrets leaving the species behind, and calls the Doctor! Repeat!
There were initial holes left in the plot as it was played out, but they were filled in as the plot went along. There were some great quotes - especially near the end ("Shuttity-uttity-up!") and the Doctor got to be brooding at parts but a genius in other parts. He even insults his past and current choices of wardrobe ("I was hoping for minimalism but I think I came out with magician.")
This was a great spacey adventure that kept us guessing until the end, and I thoroughly enjoyed it. I can't wait to view it again!