After Mildred schedules the interview for Lewis, she is holding the phone in her left hand. After Goob replaces the coffee in her right hand with his juice box, she turns into Lewis's room. The juice box is still in her hand but the phone has disappeared.
When Wilbur throws Lewis off the roof onto the invisible time machine, Lewis falls flat onto the glass dome, complete with hollow glass dome sound effects. When the time machine becomes visible however we see that the dome was already open and Lewis actually fell onto a chair. His limbs should have stopped falling at different levels than his torso.
During the memory scanner's wedding scene, Lewis recognizes Grandpa Bud because of the smile on the back of his balding head. In the next few glimpses, Bud has no hair on the back of his head, but when they get in the car together he does.
During the 'pop quiz' scene, where Wilbur is asking Lewis about all he knows about the Robinsons, Lewis refers to Wilbur's dad as 'your dad, Cornelius'. He does not meet Cornelius before this point and no one told him Wilbur's dad's name, yet he knew anyway.
When the time machine crashes Wilbur is seen holding onto the steering wheel of the time machine, clearly detached from the time machine. At the next scene when Lewis and Wilbur are looking at the damage done to the time machine we see that the steering wheel is intact with the time machine.
When Lewis is being chased by the Doris building in the scene "Doris' vision of the future", as he is attacked by the normal size bowler hats, the building turns to (perspective) Lewis' right. After going through the tunnel, the building has cut him off, but has come from Lewis' left side.
Fire sprinklers don't work as depicted in the gymnasium scene. They are set off by heat (flames) not just smoke, and only the affected sprinkler releases water, not every sprinkler in the room or building.
In the scene where the Bowler Hat Guy is trying to pass off the memory scanner as his own, he is seen carrying the memory scanner in the box right side up, and then after the introduction is seen taking the box off the top, but in order to do that, either the box would have had to have been turned upside down, or the bottom would have had to been loose, in which case the memory scanner would have fallen out.
The goof item below may give away important plot points.
The whole evil Doris scheme and the theft of the memory machine were carried out by the adult Goob who wanted revenge because he had fallen asleep as a child and missed catching the baseball. However, when Lewis woke him up and he caught the ball that changed everything and he no longer would want revenge so he would never have time traveled in the first place.