I am trying to embed a video for the show your work section. I copy and paste the code directly from You Tube, but when I go to preview my post it only shows up as code. Shouldn't the video show if that's the embed that I've chosen?

Nope. The only way to embed a video on DV Info Net is to upload using Vimeo (link: Vimeo, Video Sharing For You (http://www.vimeo.com)).