When Charles is taking the woman for a test drive in the car, Elizabeth pulls up next to them, and the boom is reflected in her door before it moves out of shot, though the boom pole is visible throughout the scene.
When Lizzie is in the restaurant with Mickey, Fred pours her glass of water into her lap. When Fred puts the glass back down on the table, you can hear that the glass is made out of plastic. A few seconds later, Fred is holding Lizzie's wrist and knocks the glass over onto the floor, which then shatters as if it was made of glass, not plastic.
After the mother goes upstairs to hide Drop Dead Fred in the box, Elizabeth goes to the dining room table to clean up and you can see a dramatic change in the corn flakes mess. When they first spill it, it is more to the outside of the table and afterward it is more towards underneath the table.
When Fred and Lizzie are making the mud pie, the amount of mud on Fred's hands changes between shots: in some, his hands are covered down to the wrists, while in others, the mud only goes just past his knuckles.