Weird Shadows

Looks to me like you're using model textures, find the texture in the texture browser and look at it's filename, it proable has model/ or prop/ at the begining, you MUST NOT USE THOSE TEXTURES because they mess up. However, fortunately for us valve make two versions of almost all their textures, so all you have to do is find the same texture that doesn't have model/ or prop/ at the front and replace all the offending faces and problem solved

Funnily enough I was going to ask the exact same question

A good way to avoid this is that when you are searching for textures, make sure to type the / at the end of the word (if its a category, look wood, nature, metal, etc). If you search wood, you'll get several props textures in addition to the ones you want. If you search wood/, you'll only see normal textures.