When Steve's girlfriend is telling him she's pregnant, the light in the room behind her goes from on, to off, to on again
The grandfather clock in the background is heard striking the half-hour medley; yet when it's shown between shots, the hands are clearly not at the 30 minute mark.
Steve Jobs and Steve Wozniak meet in the conference room the night before the IPO. When Wozniak gets up to leave the room, the notepad is on the table to Wozniak's right, with another piece of paper next to it. In the next shot, only the notepad is there.
When Jobs introduces Apple's new music player he calls it "the iPod". Jobs avoided preceding Apple devices with "the", rationalizing that doing so positioned a product as a representation of a user rather than as an inanimate object. In video of the event Jobs refers to the device as simply "iPod" without any definite or indefinite articles.
(at around 14 mins) When Woz is soldering a circuit board, he's soldering the wrong side of the board. He's also made a mess of the IC chip leads, which is precisely why all soldering is done where the contact pads are: underneath the board.
Every time Steve Wozniak solders in the move, the solder sizzles. Solder never sizzles or makes any other sound. The only time you would hear a noise is when periodically cleaning the tip of the iron on a wet sponge.
When Jobs visits a computer store in 1976 to arrange to sell first Apple computer, several IBM monitors on the shelf did not appear on the market until the IBM PC several years later.
Steve Jobs pulls into a handicapped parking space in 1980, before laws required reserved parking for the handicapped.
Just before Jobs takes over the Macintosh project in the early 1980s, a second-generation Chevy Cavalier sedan with heavily oxidized, peeling, and faded blue paint drives past in the parking lot. The second generation entered production in 1988, and it would presumably take somewhere around 24 years (when the film was made) for the paint to become that deteriorated.
When Jobs introduces the Apple II at the 1977 West Coast Computer Faire, the Apple II shown has a white square power light that did not appear until the Apple II+ model was introduced.
In the 1977 First West Coast Computer Faire scene one of the computers is a Commodore SuperPet which did not come out until 1981.