When Randy is looking at Steiner's appointment book he notes that last New Year's Eve, Steiner played a private party for Mandy Bronson. December 31, 2005 was a Saturday, but the book shows it as a Sunday. Obviously this is a 2006 appointment book.
When Randy is trying to pry his photo off of the wall in the doctor's office, he causes most of the other photos to fall off the wall, and leaves a huge hole where his photo was. A few seconds later the other photos are back up and the hole has repaired itself, with only some glue residue remaining where his photo was. It is mentioned in the audio commentary that this is the result of the scene being created from several takes.
When Monk and Natalie are in the balloon, and Mandy Bronson opens fire on them; the balloon starts to descend after only a few bullet holes are punctured in the skin. In real life, 2 or 3 bullet holes would not cause the balloon to come down, the hole would need to be much bigger, or more bullets would have had to have been fired.