Continuity mistake: The baby carrier little Sky is in as the group heads towards the car changes between takes. When they are walking down the driveway, it is open, and Sarah Jane quickly closes it when Gita comes up. Gita opens the carrier, to discover the baby, and Sarah Jane closes it again. There is more dialogue and Gita goes back to cooing at the baby. When did the carrier open again? Then the car alarms go off and if you look closely, you can see it's closed again, which is confirmed when the baby is handed off to Clyde.
Plot hole: At the end, all the things and beings that manifested from paintings or drawings are pulled back into their paintings or drawings, including K-9 from Clyde's book. But in the last scene in the Vaults, the puzzle lock can be seen still attached to the Abomination's case, even though it was manifested from a drawing in Clyde's book. The crew probably forgot to remove it after the scene where the paintings went back.
Other mistake: Mr. Smith scans the Mona Lisa and determines that it is genuine from DaVinci's brush strokes. He should have also noticed the words "This is a fake" written in felt tip under the paint, from when The Doctor replaced the Mona Lisa with one of DaVinci's "forgeries" in "City of Death."
Plot hole: When Maria Jackson is running away from the alien creature, she turns left into a metal fencing. The camera shows this seconds before she runs into it, banging on it in frustration. This does not make any sense. She saw the metal fencing, so why did she continue to run into it? Why did she not turn right instead and along the park?