When Michael Clayton spots Arthur Edens in the back alley, Arthur is carrying a bag of bread. In the beginning of the conversation, one loaf in the middle is missing its top, which apparently may have been eaten. In the following shots, the loaf is full.
When Clayton is in Arthur's loft and he picks up the red book from the coffee table, a folded slip of paper is sticking out from the bottom. A moment later, as he's flipping through the book, he almost doesn't see the paper because it's all the way inside.
After Karen and Michael's final encounter, Karen looks off in Michael's direction as he walks away from her. In the next shot, she's looking straight ahead, 90 degrees to the right of her initial stance.
Michael started with the firm in 1990, and has been there for 17 years. While speaking to Marty, he reflects on his state in life, and claims to be 45 years old. He was born in 1959, so he should be 47 or 48. He may be lying about his age.
Early in the film, during a drive in Manhattan, a tree is in vivid bloom, which occurs in Spring. The rest of the film takes place around Christmas, with lit trees and decorations. In the rural New York scenes, the grass is dead and and actors' breath is clearly visible.
The cop tells Michael Clayton about Arthur's death, "There were pills all over the place." The bathroom was flooded, presumably from the sink where the pills would have been taken. Whether they were scattered on the floor or, as the murder scene suggested, shaken into the sink, the water would have dissolved any pills in the time it would have taken to flood the downstairs. The scene included a lot of capsules, so there's a very good chance that they didn't fully dissolve.
After the bomb explodes and Clayton's car is burning, he throws his wallet, watch, and personal effects into the burning car, apparently to make it look like that he was killed in the fire. Any investigator would quickly notice a lack of human remains.