The time scale always niggles me in this episode.

When they're looking for graffiti out on the streets and eventually find some near the railway, there's a clock on the wall that shows a couple of minutes after 11.

When they get back to the flat it's clearly late because John is going on to himself about how he needs to sleep, so maybe 1am by this point?

Then they go back to the museum. Now, I know that they could feasibly gain access at any time because those places always have some security on duty throughout the night even when it's closed, but why would that guy Andy still be there? Unless they'd got his number previously then contacted him to arrange to meet him there.

Then at the police station, which is still really busy but you can kind of get away with that because the police might be working through the night too. Same at the hospital and the scene with Molly. It's believable that she could be working nights, so I'll let them off with that.

The next part that really annoys me is when they get back to the flat and get the books sent over. By this time it would realistically be about 3 or 4 in the morning. Why would Mrs Hudson still be awake and why would she think anyone was collecting for charity in the middle of the night?