When we see Clara sleeping she has her mouth shut, but the sound we hear is of her breathing through her mouth.
When the Doctor and Clara emerge from the TARDIS with a motorbike, they leave the TARDIS door open behind them. In the next shot, it has been mysteriously shut.
Perhaps people are already discussing these matters on the fora. After all, apparent errors in Doctor Who sometimes turn out to be deliberate. That's why they're all the more irritating when they're not.
Having said that, I enjoyed the rest of the show, Mrs Lincoln.