When Chris and Christopher are collecting their stuff after being kicked out of the hotel room, Christopher picks up his basketball in a grocery bag. The next time he is seen, he is carrying a garbage bag.
There are several references to "Pac Bell" (Pacific Bell) pensions. Pac Bell was one of the "baby bells" created by the court-ordered breakup of AT&T in 1984. Before that, the official name of the company was "The Pacific Telephone & Telegraph Company." Anyone who retired before that would have a pension from Pac-Tell, not Pac-Bell.
Before Chris solves the Rubik's cube, he is talking to Jay Twistle on the sidewalk near the taxi. A man in a brown jacket and tie passes by, followed by a blonde in blue clothing. A few seconds later, they pass by again walking in the same direction. When Chris runs out of the building after saying he has learned to get his job done early to make it to the shelter in time, the same man and woman appear in the distance, walking together. Near the end of the movie, when Chris learns he got the job, he walks outside, into a crowd of people walking. One of the extras walking near Chris is the same blonde in the same blue clothing.
When Chris admires the stock broker in the red sports car, the stock broker parks his car several feet behind another car. In the next shot, from across the street, the red sports car is just a few inches behind the other car. In the next shot, back to the original location, it is several feet away.
When Chris chases Hippie Girl in the BART station, he looks from the gate area down to the train platform. Hippie Girl stands next to a BART train with a "#1 Transit System in America" decal just to the left of the door. After he runs down to the platform and bangs on the closed train door, the decal is gone.
Christopher has a scuffle with the taxi driver, opens the front door, and tries to get his scanner out. When the taxi driver grabs him and tries to pull him out of the taxi, they are suddenly on the car hood (bonnet), and Christopher throws the taxi driver on the hood. In the same shot, the front door is closed again.
At the beginning, when Chris and Christopher are walking to daycare, Christopher is carrying a basketball in a plastic grocery bag. In subsequent shots, he is not holding the ball. He receives the same ball as a gift later in the film.
When Chris enters the firm for the first time, covered in paint, he turns the corner of cubicles while following the assistant. A crew member in a green shirt, black pullover, and red hat, retreats behind a pillar underneath the stock ticker.
In one scene, the train doors close on Chris Gardner's hand while he is holding a bone scanner. He doesn't let go, and the train departs with the doors partially open. That would never happen in real life; BART trains are designed not to move if the doors of any car are obstructed.
When Smith purchases a new lamp for the scanner and is on the bus, he holds it up to the camera and shows it to be a Xenon tube, the sort used for strobe lights and camera flash. Later on after he repairs the scanner and switches it on, it shows as continuously illuminated. This type of lamp is a high speed discharge lamp that can only flash and lighting it continuously would melt it in seconds.