Moviemistakes.com has rounded up a blog post with fifteen of the movie’s most obvious mistakes. These include car writing changes, disappearing/appearing objects, fast forward clocks etc.
NOTE: Possible spoilers ahead.
Mikaela gets a tow truck to move Bumblebee after he lost his legs. At first, the writing on the left door says “Mike’s Towing - 800-555-0199″. When she gets out to hoist Bumblebee up, the writing on the same door has changed to “Mike’s Towing - 800-333-MIKE”.
At Hoover Dam, when the soldiers salute Keller the clock reads 10:00, then as Keller, the soldiers, Maggie and Glen walk away in the background, when Simmons tells Sam that they got off to a bad start the clock reads 11:35, and next shot when Banacheck interrupts it reads 11:43. Also when Simmons talks to Mikaela and Sam the word “Nevada” is gone and it only reads “Time” under the clock. Then when Banacheck says, “Come with me, we’ll talk about your car,” the word “Nevada” is back under the clock.
After class when Sam rushes to his father, who is waiting in his car, and tells him that he got an A-, the license plate is affixed to the front bumper. At the start of the next shot, the front license plate is gone, but it then reappears when they arrive at Bobby B’s.
You can find more mistakes on the original moviemistakes.com post.