When Bobby and Mikey's family first arrive at their new house in California, the king rips off the sign by the door that says "The Marshalls" (at around 50 mins). The sign reappears in the next shot and then disappears again when the king comes back out.
When Mikey and Bobby are running through the sewer, both of them fall several times into the dirty sewage. However, there is no sign of grime or sewage on their clothes when they face the bullies.
At the end of the movie when Mike talks about going to college, you can see the postcard that his brother sent him years ago. But as the postcard turns around, you can see that although the message is the same, its obviously not the same one in the previous scene. The original one (at 105:19), it is in black ink, has two circles and a square in the cancellation mark, has "jeronimo bill" split across two lines, and is signed "Boddy". At 105:29, it is in blue ink, has one circle and a square in the cancellation mark, has "jeronimo bill" on one line, and is signed "Bobby".
When they first arrive to find that Bobby has flown away, the walkie talkie antennae is bent. When they show Mike and his mom it's straight again.
(at around 36 mins) When The King finds the electric cord inside the oven he closes the door after pulling it out. When they show it again as he grabs his beer, the door is open again.
When they take the Radio Flyer airplane to Fisher's gas station, Fisher fails to turn the crank on the right to reset the gallons/dollars digits.
When Bobby and Mikey are in the comic book store, Mikey picks up a "Monsters" comic book with Dracula on the cover, and a Transformers comic is behind it, Transformers was not created until mid-late 80s and this movie was based in the mid/late 60s.
The sheriff's Bronco has BFG All Terain T/A tires not made until 1976.
When the boys are at the movies they are watching The 7th Voyage of Sinbad (1958) and Chitty Chitty Bang Bang (1968). These movies are 10 years apart.
Buffalo Bills Amusement Park was said to be in Oklahoma, but the area was covered with Joshua Trees which only grow in the Mojave Desert.