Continuity mistake: When De Niro first meets Nolte's lady-friend, they are having a conversation in a bar or restaurant. As the camera goes from De Niro to the woman, the woman's top blouse button is open in one shot, then closed, then open, etc.
Continuity mistake: When Sam is talking to the P.I about "Taking care of Max," he gets into his car and the window is up. A few seconds later, the window is down. There wasn't enough time for him to roll it down. (00:54:50)
Continuity mistake: After Max Cady killed Kersek and Sam Bowden finds his corpse in the kitchen, the blood pool changes shape in two different cuts.
Answer: He snuck in during the day and hid, before Kersec's teddy bear security system was set up. Sam Bowden realises this when he wakes from a nightmare. Its how he was able to poison the dog which hadnt been let outside. Max Cady killed the maid in the pantry with the same piano wire he later attacks Kersec with.