Continuity mistake: At the end of Rocky IV, Rocky's son Robert is around 6 or 7 years old. After Rocky comes back from Russia in Rocky V, his son is around 12. While there was a 5 year interval between Rocky IV and V, no time had elapsed from the two in movie time. So, therefore, his son should still be the same age given that Rocky has just recently fought Drago, "The Russian" considering his bruises, and they all returned home right after the fight.
Continuity mistake: When Rocky and Paulie are giving advice to Rocky Jr, they stop for a second in front of a foreign looking market. Then they cross the street. At that point, the market is covered in shade, and the sunlight is on the other side of the street. Seconds later, the shot changes, and the market's side of the street is suddenly the sunny side.
Continuity mistake: During Rocky's "thinking" drive he takes in Rocky IV, his license plate sticker had an expiration date of 1986, which means the time frame for Rocky IV was 1985-ish. However, after Rocky comes home from his fight with Drago (which was only about a month's time span) and has the difficulties with his family we see in Rocky V, his son and their friends can be seen watching Christmas Vacation, which came out in 1989, over 3 years later.
Continuity mistake: Right at the end after Rocky has defeated Tommy Gunn and George Washington Duke is taunting him Rocky leans down to one side in order to uppercut GWD. In the next shot the punch comes from the other side, ie the "raised" side. No matter how hard his punch is, he couldn't raise GWD off the ground and knock him out with the way his body is twisted.