When Daniel and his Mom first leave Newark you can clearly see a big dent on the tailgate of the station wagon as his friends chase the car. Later,when his mom picks up Ali at her house, the dent is gone as they push the car to get it started. A better view is visible when his mom picks them up at the "Golf n Stuff". This was several months later after they left Newark but his mom would have surely fixed the starter problem before the tailgate.
When Miyagi and Daniel are sitting in Miyagi's house and talking about his wife Miyagi gets up and pours himself another drink, the bottle he picks up still has the seal on it and it remains unopened as you hear the distinct sound of the liquor being poured into the glass.
When Daniel picks up Ali for their first date and his mother's station wagon won't start, they push start it and ask Ali to "pop the clutch", however you can hear the starter is used to start the engine.
At the part where Ali trips the members of the Cobra Kai at the Halloween dance, if you watch closely you can see the one Cobra Kai crack a smile as he falls for a brief second. Watch the one on the far right side of the screen as he falls on the other.
After Miyagi rescues Daniel on Halloween, he serves him a cup of tea. When Daniel grasps his cup by its sides, Miyagi insists that he instead support the cup from the bottom. However, the next time Miyagi drinks, he grasps his own cup by its sides.
Daniel's has cuts and scrapes (from getting beaten up the day before) during the "wax on, wax off" scene at Mr. Miyagi's house. His wounds disappear when he and Ali go to Golf 'N' Stuff and reappear the next day in time for the "sand the floor" scene at Mr. Miyagi's.
During the last fight scene with Johnny and Daniel, Johnny's black head band falls off in one shot, and the referee picks it up and throws it off the mat. Subsequent shots show Johnny still wearing the head band, and some shots have him without it on. Also during the final fight, Johnny's hair alternates between being dry and soaked with sweat.
In the Country Club dance scene, as Ali dances with her father, we see Johnny take a seat next to Ali's mother. In the same shot, Ali asks, "Hey Dad, what time is it?" The shot switches to the opposite viewpoint, and the father replies "Well, it's about, uh...9:40" just as Johnny and the mother dance into the shot from the right side of the frame. They could not have arrived there so quickly from where they were seated. (This occurs around 1 hour and 21 minutes into the film.)
In the scene where Daniel arrives at Miyagi's place and discovers a note from Miyagi telling Daniel to paint his house, the opening shot is from inside the house and you can see the writing on the note Miyagi left for Daniel. The next shot is of Daniel reading the note from outside the house, and the writing is clearly different. This is because they likely had to shoot that scene multiple times, and once Daniel got mad and crumpled up the note the first time, they couldn't use it for the next take so they had to make a new one.
When Daniel and Ali are talking on the soccer field you see two soccer balls in the background by the cheerleaders. They then cut to a closeup with Daniel and Ali talking. When the camera cuts back to the cheerleaders, the two soccer balls have disappeared with only one of them coming back yet it comes back on the left of the screen.
At the costume party, Ali holds the flower in her left hand and starts to push it through the shower curtain of Daniel's costume. In the next shot (inside the costume), she is holding the flower in her right hand.
When Daniel meets Ali in the cafeteria line the day after the beach fight she has her hair in a thickly curled style that is different from what she wears in every other scene, even those allegedly later that day.
During the Halloween Dance, Bobby and Tommy both have their hair coming out of the caps of their skeleton costumes. Tommy can be seen at the right dancing with a bunny with his hair out of his costume. Bobby has his hair showing when he goes into the bathroom to find Johnny. Before Johnny runs out of the bathroom you and see that they are fixing their caps to show no hair coming out. When they run after Daniel and fall on the floor Tommy's hair is out of his costume again. After running and jumping a fence to catch up with Daniel their hair is back behind their costumes.
When Daniel and Ali are talking on the soccer field you see two soccer balls in the background by the cheerleaders then they cut to a closeup with Daniel and Ali talking when the camera cuts back to the cheerleaders the two soccer balls have disappeared with only one of them coming back yet it comes back on the left of the screen.
When Mr Miyagi is showing Daniel that he has been learning karate the whole time, he says, "Show me paint the house." He is holding Daniel's right hand, but in the next shot Daniel drops his left hand.
In the scene where Daniel catches the fly in the chopsticks, for the first few cuts, the fly is somewhere in the middle of the chopsticks and the chopsticks cross each other past the point where the fly is being held. In a later angle, the fly is held between the very tips of the chopsticks and the sticks do not cross each other over their entire length. He never drops or releases the fly and re-catches or picks it up, so the fly was clearly moved between takes.
When Daniel puts the hose in the bathroom stall to get revenge on Johnny, he clearly places it over Johnny's head. He then turns the water on, and runs out. But when Johnny runs after him moments later, both his hair and clothing are dry.
In the beginning scene when Daniel and his mother are driving away down the street, they are said to be leaving Newark NJ. However that street is actually in Harrison NJ and is also a "one way" street going the opposite way. Harrison is a neighboring town.
The newspapers that Miyagi saves are over 40 years old. They are not in plastic, and yet they seem bright and new. They should be yellowed, old, thin, frayed, torn, creased and have little holes in them.
In the scenes showing Mr. Miyagi wearing his Army Uniform, the award ribbons are incorrect as the ribbon signifying the Medal of Honor is always worn at the top and on a row by itself. It appears to the left on the first row.
When when Mr. Miyagi is drunk and singing, he shows Daniel the picture with his pregnant wife. Immediately after he is pouring himself another drink. You can see the that bottle top is still on and the red seal is not broken on the bottle.
At the end of the movie, as Daniel is advancing through the tournament, the logo on the back of his robe appears on the card his name is on, even though they had no advanced knowledge of the logo. However, Mr. Miyagi (or even possibly Ali) could have brought a copy of it for the tournament staff to use.
When Miyagi and Daniel go to the Cobra Kai dojo the day after the Halloween dance, Johnny is seen with a black eye. However, when he fought Miyagi the night before, Miyagi blocked Johnny's punches, flipped him, and gave him a chop to the stomach, never hitting him in the eye.