My alchemy lab: Where did it go?!
http://i121.photobucket.com/albums/o224/rx_digital_78/Image12.jpg

My non-working weapon racks:
http://i121.photobucket.com/albums/o224/rx_digital_78/Image14.jpg
http://i121.photobucket.com/albums/o224/rx_digital_78/Image15.jpg
(Proof of equipped item...)
http://i121.photobucket.com/albums/o224/rx_digital_78/Image13.jpg

Also, I've been running around with an arrow and an ice bolt lodged into my head for hours now:
http://i121.photobucket.com/albums/o224/rx_digital_78/Image16.jpg

Any idea why these things aren't functioning correctly?

are you on a console?

Yes.