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.
Chosen answer: There was never 1 movie that spoofed Die Hard but they were spoofed in many movies. Here is the IMDB link where you can see all the movies they were spoofed in: http://www.imdb.com/title/tt0095016/movieconnections.
SAZOO1975