Fancy brings Buddy a glass of tea by the fence. He drinks half and gives it back to her. A few moments later when he smashes his thumb, the glass in Fancy's hand is full again.
Cage was supposed to be an ex-Marine but he's wearing a bizarre-looking quasi-military uniform that doesn't belong to any of the branches of the Armed Forces with the rank insignia of both Army Private 2 and Specialist 4 along with a checkered tie and two Army marksmanship medals.
During a shootout with a suspect, police would not stop firing even after hitting the subject multiple times if he is still pointing weapon(s) at them.
When Nicolas Cage's character presents a bag with $20,000 in 1988 you can see it is the newer "big face" $20 bills that weren't released until 2003.