When Adrian is in the coma, Rocky's facial hair is used to give a general idea of time. Just before Adrian comes out of the coma you can Rocky with almost a full beard. The shot pans over to Adrian opening her eyes. When the shot pans back to Rocky, he barely has a 5 o'clock shadow.
When Rocky is running in the park with the kids, he hurdles two park benches and then, via editing, he hurdles the same two again to make it look like four total.
As the ambulance is headed toward the hospital, it is being closely followed by a news van, no more than one second behind. When the ambulance makes a right turn down a side street, the news van is nowhere to be seen. But when they pull up to the hospital, the news van is right behind the ambulance again.
When Rocky and Apollo are on the canvas at the end of the fight, Adrian and Paulie are at home standing up in front of the TV yelling for Rocky to get up for the entire count. When he finally gets up, they show them jumping up out of their chairs as if they have been sitting through the count.
During the "Gonna Fly Now" training scene. Rocky is running through the city. He makes a left turn down a very crowded street. As he turns there is a golden coloured Gremlin parked on the opposite side of the road. In a subsequent front-on shot he is shown running much further down the road but he passes the same Gremlin once again.
During the fifteenth round, Rocky lands a left hook and Apollo Creed is knocked down. Rocky falls as the result of his own punch. The referee begins to count both fighters out. The referee would only be counting Apollo Creed out because Rocky's punch knocked him to the canvas. According to the rules of boxing, Rocky should not be in danger of being counted out because he was not struck by a punch. Rocky was off balance and so the referee would rule it as a slip.
When they show a long shot of the ring right before round 3, the scoreboard above the ring still shows it to be round 1.
The TV show that Rocky turns on for his turtles was obviously a scripted broadcast by Brent Musberger. The script he reads says the Rams beat the Buccaneers in overtime 13-10 on a Frank Corral field goal. There was no such Rams-Buccaneers game in 1976.
When Apollo is in the office attempting to set up a rematch, he calls Tony Burton's character by the actor's name. At this point he wasn't credited as a named character, but starting in Rocky III he's known as Duke, not Tony. The character's official name is understood to be Tony "Duke" Evers. It's not uncommon for actors in the Rocky movies to use their given names as their characters' first name (Frank in the meat plant is played by Frank McRae, Pedro Lovell plays Pedro "Spider" Rico, etc.)
In Rocky III, Mickey is buried in a Jewish funeral. In this film, when Mickey enters the hospital chapel, he crosses himself and later prays without donning a hat or skull cap. He was probably just doing this to be respectful in the church and to not be "out of place" when consoling Rocky.
When Rocky and Adrian meet with the real estate agent to buy the Townhouse, as they're about to walk in the front door, Rocky taps on the address numbers and says that they almost add up to 9 which is a good omen. The address is 2313 which does add up to 9, not almost 9. However, this was clearly one of many small things written into the script to show Rocky's lack of education and intelligence.
When Rocky is bathing Butkus in the bathtub of his home, the towels are embroidered with the Holiday Inn logo. This may indicate that the scene is a "pick-up shot", possibly filmed in Sylvester Stallone's own hotel room. However, it may also just indicate that Rocky had stayed at a Holiday Inn at some point and stole the towel, which was common in those days.
At the end of Rocky I, Rocky punched Apollo in the right ribs. But when both of them meet in the hospital in Rocky II you will noticed Apollo is holding his left ribs. But they exchanged blows all across their bodies, so it's not unthinkable that both sides of his body would be in pain. We also don't see the entire fight in the first film, so he could very well have been hurt by Rocky there "off camera."
While the kids are running with Rocky through Philadelphia, the group runs around a fountain. If you look closely several children fall and get trampled on by the crowd.
When Micky is watching television, his feet do not move at all, and you can tell it is a still image super-imposed on screen.
Adrian's hairstyle is noticeably different and Paulie is thinner than in the previous movie, even though it's supposed to take place directly after the end of the first movie.
When Apollo delivers his "You're goin' down" line to Rocky in the big fight near the end, it's a mirror image (identifiable by the "Superfight II" poster in the background having reversed lettering).
Although Adrian is in a coma from bleeding and complications of childbirth, she is not hooked up to any IVs or monitors in the hospital.
Despite being a left handed boxer, it is completely possible that Rocky learned how to write with his left hand.
The film takes place from New Year's Day to Thanksgiving Day, 1976. However, when Rocky is at the old Pontiac dealer at Broad and Pine Street in Philadelphia, the green car in the showroom and his new car are 1979 models.
When Rocky turns the TV on for the turtles, Brent Mussberger is talking about the Rams and their field goal kicker, Frank Corral. The plot of the movie has the time line at mid to late 1976 (Apollo's trainer, Duke, mentioned a couple of scenes earlier that about 6 months had passed since the first fight), there is a problem because Frank Corral did not play for the Rams until 1978.
When the referee is talking to Rocky and Apollo at the beginning of the final fight, his lips don't match what he's saying.
When the first Rocky fight ends, they are in the Spectrum in South Philadelphia. At the beginning of Rocky II the ambulance is coming down off the Girard Point Bridge and heads up S. Broad Street and goes by the Spectrum, again. They would have had to go over the bridge and turn around to go pass the Spectrum on their way to Jefferson Hospital.
In the first fight depicted in the first film, which also shown in the beginning of this film, Rocky's right upper lid gets hematoma and they cut it. And when Mick tests Rocky's sight, we clearly see that it's the right eye that has vision problem. But during second fight, when Rocky is first knocked-down the commentator says that Apollo has hit the damaged left eye, which was cut in the previous match.
It's well established that Rocky is left handed, however when he signs an autograph for the nurse and for a patient outside the hospital at the beginning of the movie, he uses his right hand.
Mickey wants Rocky to fight right-handed, but most of his training favors his left arm.