After Dr. Saroyan allows Finn to go to lunch early to talk to Michelle, Finn takes the glove completely off of his right hand. In the next shot, he's still in the process of taking that glove off.
The body was too swollen to ID by sight yet the clothes still fit perfectly.
The item Dr. Brennan identifies as a "Mesopotamian basin" is, in fact, a Greek type of bowl known as a Lekanis.