Charlie's father works in the Smilex Toothpaste factory. Smilex was the deadly poison gas used by the Joker to kill people in Batman, also directed by Tim Burton. See more...
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Factual error: In the scene in the glass elevator, when Mike Teavee wants to push a button, he presses the TV Room button. The elevator stops going down and immediately moves horizontally. The characters within the elevator are thrown against the wall from the sudden change. However, they are thrown against the wall that is in the direction the elevator is now moving, instead of the opposite wall as they should have been.
Continuity: When Veruca is choosing a squirrel, she heads for the last one in line, furthest from the ladder. Then after it cuts away and back, she is headed towards the middle of the line, but then she is headed for the last one again. When the squirrels jump her, she is about 1/4 of the way down the line, starting from the ladder.
Factual error: In the scene where Wonka is flashing back to his childhood, he finds a chocolate that fell beneath the fire grate in the ash. He opens it and eats it unscathed. Knowing that chocolate can melt around even the slightest heat, there is no way the candy would have survived the heat from the fireplace being just inches away.
Factual error: In the scene where Augustus Gloop gets stuck in the pipe from the chocolate river, there are two shots that show the pressure in the pipe is too great and one of the seals of the pipe burst out some chocolate. This could not happen because the machine on the ceiling sucks the chocolate up. In order for the pressure to build up underneath Augustus for the seals to burst there would need to be a machine in the river pushing the chocolate up.
Plot hole: In the end of the movie, when Willy Wonka decides to visit his father, his father does not recognize him until he looks at his "rare teeth." But the wall of newspaper printings that Charlie was looking at included a recent enough picture of Willy that the father would have definitely recognized him, before seeing his teeth, as Willy doesn't look like a normal person with that outfit.
Continuity: When the factory gates open for the contest winners, the shadows in the courtyard change between shots. [This is a reference to the first film in which the shadows shift a lot. It is also shown in other parodies of the original film, eg, the Family guy episode "Wasted talent". Still a valid mistake.]