Continuity mistake: When Howard is almost done moving out of his mother's house, there is a table in front of him with a measuring device in the top corner. In one shot, the device moves to the opposite corner of the table. In a few shots later, the item returns to its original position.
Revealing mistake: Throughout the series much is made of the fact that Howard's mother is grossly obese, and in The Engagement Reaction (S4 E23) it is even mentioned that her arms are hugely oversized. However, at the end of this episode we see her arms when she grabs Raj to stop him climbing out of the window, and they are the arms of an average-weight woman - they aren't overweight at all.
Continuity mistake: Sheldon is sitting by himself at a lunch table with an opened bottle of water with the bottle cap in front of the bottle. Raj and Howard arrive, and in one of the shots, the bottle cap moves closer to the bottle by itself.
Continuity mistake: Sheldon is taking composition books out of a box that was sent to him. When he first starts pulling them out, he has two composition book in one hand. Two shots later, he has only one composition book in his hand, but he is picking up a second one.