I have purchased Proudspire Manor in the city of Solitude. I have unlocked 2 of the 3 doors into the Manor however the back door into the manor will not unlock. The game keeps telling me that the lock can't be lockpicked and that I need a key. I do have the key in my inventory and I have unlocked the other 2 doors. Is this a glitch or is it just me?

This happens if you enter the house before becoming Thane of Solitude.

To avoid the glitch, load an earlier save, buy the house & all upgrades (to avoid the unusable weapon rack, bookshelf, etc. glitch), then become Thane. All of the doors to the house will be automatically unlocked. I haven't come across any other way to fix the glitch.