When Bernie is driving up to Mrs. Nugent's home, there is a close-up of the Texas State Registration sticker on the front windshield of the car which clearly says "12, 11" indicating that the registration will expire in December of 2011.
(at around 1 min) When Bernie is on the phone with Lloyd, there's an Apple Macbook Pro (Second Generation) in front of him. The Second Generation Macbook Pro didn't come out until late 2008 and the murder took place in 1998.
When giving the confession, Bernie talks about fantasizing of her dying in accidents and mentions her falling down an escalator in the mall in Longview. In reality the Longview Mall is only one story and does not have an escalator.
The goof item below may give away important plot points.
After the sheriff and Mrs. Nugent's granddaughter pick the lock to the front door to get access to Mrs. Nugent's house to search the house, one of the searchers goes out through an unlocked glass door to the patio. If they really had been locked out of the house the patio door would have been locked also.