I am trying to complete this TG quest. But, Mercer will not unlock the door for me and the door tells me there is a key required. Does anyone know if this is a known bug, or if there is a key I can get. The sources I've found on UESP and the Wiki seem to indicate that Mercer will unlock the door but I've exhausted all the dialogue options and he just stands there.

I haven't done this quest on my latest char (will be 2nd time through) but I do seem to recall at least one place where we stood around for some minutes before anything happened. If this is the old Nord puzzle door, I recall Mercer saying how people are easily impressed by them, but that they open easily enough if you have the knack. He barely paused to activate it and it was open.

If you have a follower in the way he won't walk up to it and unlock it, just manouvre your follower out of his road.
The door will still say it needs a key after he unlocks it though, just ignore this and head on in.