Continuity mistake: Rocky's eye was injured at the fight in the beginning of the movie. They show the right eye covered up with the bandage at the hospital, but no one says specifically which eye it was. When Rocky decides to fight Apollo again he goes to see Mick. Mick the trainer tests both eyes. He tests the left and it tests OK, then he says, "Now we try the other lamp." The right eye is the one that has no peripheral vision. Mick slaps him on the right cheek to prove how he would get hurt by Apollo. When he does train him, Mick tells Rocky to switch to fighting right handed. Mick says,"Now, this will confuse Apollo, and it will protect that bad eye." However, in the fight at the end the announcers says that, "Apollo hit that bad left eye, remember from the first fight. It's the same eye that was cut the last time." (00:47:40 - 01:43:15)
Continuity mistake: During the final part of the "gonna fly now" scene, the number of kids around Rocky is inconsistent between shots as of when he jumps over a bench and when he is walking up the steps.
Continuity mistake: When Rocky sees his baby boy, he keeps swapping from head covered / uncovered and messy / brushed hair between shots.
Factual error: In the opening scene, the ambulance takes Rocky to Pennsylvania Hospital, whose ER is between 8th and 9th Streets, on Spruce. The ambulance is shown turning off Broad, onto Market Street, then back to 8th, and then down 8th to Spruce (presumably) to get to the hospital, when it could have just made a right at Lombard or Locust. (00:01:59 - 00:04:01)
Factual error: Rocky buys and drives a Trans Am. Later, we find out that he can't read after his commercial goes horribly wrong. He couldn't have a driver's license because he would need to pass the written test first. You can't take the test if you can't read the questions or the driver's manual for that matter.
Suggested correction: It's not that he can't read at all, he just reads slow and has some trouble. It may or may not be enough to hamper him from taking the test. But is it ever established that he has a driver's license? He wouldn't be the first person in Philadelphia to drive without a license.
When you can't tell the difference between simple words like rat and cat, there's a pretty good chance you can't pass a written driver's test, which is why I said he "couldn't" have a license.
Revealing mistake: In the fight against Apollo, Rocky's last punch of the second round conspicuously misses by a mile, but Apollo nonetheless acts like he has been punched, and there is a punch sound effect as well.