When Rapunzel and Pascal were playing hide-and-seek, the flower pot outside the window is shown with a painting of a flower. In the later parts of the film, no painting is seen there.
In the final tower scene, when Flynn/Eugene reaches for Rapunzel's hair, his right hand is unshackled. A second later, it's shackled again.
The painting on the floor of the tower, showing a man with pointed teeth, disappears and re-appears.
The strand of hair that falls across Rapunzel's face as she is pleading for Flynn's life disappears.
During the first verse of the song "I Have A Dream" (in the "Snugly Duckling"), the hook-hand thug hooks the keys out of the piano and they are sent flying across the room. In the next shot, he continues to play the piano as if the keys were still there.
All ships in the harbor are clearly at anchor and unmoved despite the light wind (clearly seen in the lanterns scene). Yet, all of them are in full sail, which is clearly a mistake, even for an animated fantasy movie.
Rapunzel tosses her hair over a hook and to the ground to hoist Mother Gothel to the tower window. The dangling hair, the baskets of supplies, and a grown woman together would surely outweigh a willowy teenager, and such a hoist would be impossible.
As "Mother" stabs Eugene after he climbs the tower to rescue Rapunzel, the knife comes out clean, no blood. However, blood on the knife would likely be reason to increase the MPAA rating to a PG-13, so to keep the rating at a PG, the blood was omitted.
When Rapunzel and Flynn arrive at the lantern festival and cross the bridge, Rapunzel looks back to the camera and exclaims "Wow!" but there is no voice to the word. Actually, she's not exclaiming - she's mouthing the word silently, because she's so stunned by the view.
Rapunzel's hair is just long enough to pull Mother Gothel up, but it is also long enough to lower Rapunzel to the ground, which would take twice as much hair. However, it is seen that Rapunzel loops her hair over hooks when pulling Gothel up, which would allow for half the hair to still be in the tower, with just enough lowered to serve Gothel.
When Flynn and Rapunzel are in the cave, it is filling with water, despite the fact that their heads are in a small pocket of air higher than the water level. There's no way the water could fill up to cover their heads if there was nowhere for the air already in the cave to go. Given that part of the cave wall is simply composed of stacked rocks, there are plenty of cracks for the air to escape through.
When Flynn is hiding from Maximus in a cave, Maximus can be seen looking behind him. Horses have to turn their whole neck to look behind them, but Max turns his head like an owl would. However, Maximus exhibits "super-horse" and non-horse abilities and behavior throughout the movie, most often those of a dog. Such discrepancies are just part of his character, to make him funnier.
When Flynn is first rescued by the thugs in the tower, his shackles disappear as he runs away.
When Rapunzel first leaves the tower, she steps in a small pool of water. She then turns 180 degrees to watch a bird flying overhead. In the next shot, she just walks on forward, even thought she would likely first have to step out of her own hair, which would have tangled around her when turning like that.
In the song 'When Will My Life Begin', Rapunzel is seen holding a guitar without a strap by the neck (fretboard). She wouldn't have been able to hold the guitar without any other support.
Flynn Ryder is seen wearing spur straps throughout the entire movie, yet is never seen wearing spurs. Also, the straps have no buckle on them, leaving him unable to fasten them.
The film is said by the creators to be set circa 1780, yet we see Rapunzel using a match to light candles. The first modern, self-igniting match was invented in 1805 by Jean Chancel.
Rapunzel can swim, despite having been locked in a tower her whole life.
Maximus found the secret passageway, despite the fact that he didn't see the pub thug showing it to Rapunzel and Eugene.
How did the castle staff verify Rapunzel's identity when she returned as the Lost Princess?
When Mother Gothel is falling from the tower, her hands look young, even though she is turning to dust, and her hands were shown to become old-looking even before she starts to fall.
When Flynn is dying, he is on his back with his right hand palm up on the floor. Later when we see both lovers from far above (when the magic is working) his right hand is palm down. If Flynn is dead, he wouldn't be able to change the position of his hand.
Gothel foolishly continued to celebrate Rapunzel's birthday on the correct day, even though the baby then toddler wouldn't have noticed any difference, and of course that's when a huge flying lantern show took place every year for the missing princess.