Continuity mistake: After the Doctor is knocked unconscious, Clara uses the psychic circuitry to pilot the TARDIS to what turns out to be a moment in the Doctor's past, in the barn first seen in "The Day of the Doctor." The loft in the barn where the young First Doctor is sleeping in bed, however, was not present in the previous episode.
Suggested correction: These events take place thousands of years apart. Buildings (especially wooden ones) are likely to change in that time.
The barn appears three times, in "The Day of the Doctor", "Listen" and "Hell Bent." Its appearance in "The Day of the Doctor" is chronologically in-between its appearances in "Listen" and "Hell Bent." Both of the two latter episodes have the loft, but "The Day of the Doctor" doesn't. That's the mistake here.
Continuity mistake: When Danny is saying "Straight to dinner", the shot switches from one facing him to one facing Clara. In the first shot, Clara is holding up her glass, but in the second shot her glass is suddenly lowered before she raises it again. (00:03:52)
Continuity mistake: When the Doctor shows Clara the "listen" written on one of his blackboards, the handwriting is different to when it was first shown. (00:07:07)