Corrected entry: When Buddy is decorating Gimbel's after the store closes, you see a sign that says there are security cameras watching you. When the supervisor tells them someone is after his job, he explains that he doesn't know who did it. They could easily look at the cameras.
Correction: The sign states "There are security cameras watching you." They may just be live-feed cameras. They aren't necessarily being recorded where they can go back and watch it. Maybe it's just a live feed and nothing more.
Corrected entry: After the snowball fight in the park, Buddy and Michael are walking by a row of houses. Under the steps of one of the houses, you can see a man in a yellow coat come out, see the camera, and then turn around to hide from being seen in that shot.
Correction: I don't think the man was dodging the camera. Even people in New York forget things they may need to go back into their homes for.
Correction: We see Buddy easily avoiding the security guard. It's reasonable to assume he obscured the cameras as well.