I just did my house in Windhelm.

Just checked the bedroom and the bed, bed side table, and small wardrobe are all like moved up from where they need to be. The bed is off the wall and the small wardrobe is sitting in a shelve with potions on it.

There seemed to be something I could click on behind the bed thats invisible. I think I forgot to click something when doing blood on ice? Is there anyway to fix this?

You have to be sure to click on all the "investigation target" things when doing blood on the ice, or it will be wonky.

I currently have no chest at the foot of the bed, because I didn't investigate the bedroom.

I finished blood on ice, but I have a save from two hours ago before I got the house Do you think if I go investigate after the mission but before buying it it will be alright?

whoah, you learn something new every day.

OOHHH! is that what causes that? I have always felt there should be another chest somewhere in the Windhelm house.. well actually, my Windhelm house does not have any chest at all...

Can't say for sure, I don't remember if you can still "investigate" things after you've finished that quest. Still, it couldn't hurt to try!