Visible crew/equipment: When the car and truck drive upto the building, the truck goes down a ramp - another moving shadow can be seen cast over the car, from the camera crew.
Revealing mistake: When John jumps off the roof with the hose tied around him, you can see that the stuntman's hair is slicked back with fireproof gel during the explosion.
Other mistake: McClane's undershirt is white for the beginning of the movie, but when he emerges from the air conditioning ducts, it is now a dark colored shirt (it looks very dark green) with a lot of stains on it. If this is supposed to represent the same shirt, just very dirty, it could not have come from the A/C duct work, for it was all brand new and the interior shots showed it all to be spotlessly clean. The change in appearance is far too abrupt to be possible.
Answer: Most large companies, particularly hi-tech or multinational ones, require visitors to check-in, especially afterhours. By having John search for Holly's name, it can be verified that he actually knows someone who works there, that there is an actual employee with that name, and otherwise assess whether John is a legitimate visitor. This scene's real purpose, however, is for plot exposition. John learns from the monitor that Holly now goes by her maiden name (Gennero) rather than her married surname. We see John's annoyed reaction to learning this, which sets up a later confrontation between him and Holly over their troubled marriage.
raywest ★