As James was examining the handwriting of the two papers before him, his hand brushed the left hand one, causing it to twist slightly counterclockwise on the desk. A moment later, it's suddenly straight again. When the camera angle changes again, it's back to being askew.
The actress playing the dead grandmother (Phyllis Somerville ) inadvertently moves after her character is killed by the exploding gift. While Detective Eames (Kathryn Erbe ) is leaning over her dead body, Somerville's moves her hand while it's on her stomach.
James' mother was named Betty Bennett. "Betty" is a variation on "Elizabeth," so when James wrote her signature, he was forging his mother's signature. Indeed, he told his mom at that point that her signature was the first one he learned to forge.
At the end when James showed off his ability to easily forge signatures of real, famous people, among the names he wrote was Elizabeth Bennett. But, Elizabeth Bennett was a fictional character in Jane Austen's masterpiece Pride & Prejudice. She had no signature because she was not real.