When Pee-wee enters the magic shop, the image is flipped (most likely to facilitate being able to read "Mario's Magic Shop" on the shop door), as a result, the hanky in his left-hand suit pocket is switched to the right.
At the beginning of the chase scene on the studio lot, the security carts are unplugged from the wall as if they were electric carts, but then they are heard making noises as though they were gas-powered.
The Criterion theater, in the mall that Pee-wee goes to, advertises that they will be showing something called "Cartoon Cavalcade." But a few seconds later, in a reflection, the theater sign is promoting an entirely different feature. When he starts walking off not long after this the Cartoon Cavalcade signage is back.
In the bicycle chase scene where a studio guard pursues Pee-wee, the guard pulls one of the tassel handles off Pee-wee's bike. In the close-up shot, Pee-wee presses a button that causes a handle without a tassel to spring out. When they cut back to the wide shot, the tassel is back as well.
When Pee-wee leaves the park and is driving his bike down the road, there is a red classic Mustang on the right side. In the next frame, we see Pee-wee coming down the same road from the same angle, but there is now a blue car where the Mustang was.
As Pee-wee is rescuing the animals from the burning pet shop, He brings the dogs out and tells them to "sit." In a close up shot, they in fact do sit on command but in the very next shot from further away, the dogs are all scattered about the sidewalk walking around.
When Pee-wee is driving Mickey's car past the road warning signs, the signs are clearly seen attached to carts on rollers coming towards the camera. This is only visible in unmatted full-screen home video.
The Car Mickey was driving, was either registered to him or even more likely stolen. The Police should have known by the car and license plate number that it was either Mickey's car or a stolen car making their disguises irrelevant.
When Mickey and Pee-wee stop for the police road block, Mickey shifts the car into park when they stop and then hides his hands (with the cuffs) in between his legs. After the conversation with the officer, Mickey never lifts his hands out from between his legs to shift the car back into drive to move forward.
While making breakfast, when Abraham Lincoln flips the fourth and final pancake which sticks to the ceiling, you can see the pancake hit the ceiling and bounce to the side, revealing that the filmmakers simply dropped pancakes on the floor then inverted the shot.
As Pee-wee and Mickey drive away from the police checkpoint, the road is marked with a solid white line on the right shoulder, and a double yellow line on the left shoulder: these markings denote a unidirectional 2-lane highway. In the very next cut, the white line is on the left shoulder and the yellow is on the right. They are now going the wrong way.
The goof item below may give away important plot points.
When Pee-wee is dropped off by Large Marge at the truck stop, folks at the diner there inform him that she was really dead. They point to a plaque with her picture saying she died that very night 10 years ago - January 11, 1974. The weather throughout the movie shows lots of green vegetation, and living plants, not the characteristics of January weather.