When Snow White decides to clean the dwarfs' house, she takes off her cape and hangs it on the wall. When the dwarfs return from the diamond mine later and are shocked to find the house clean, the cape is gone and it never returns for the rest of the movie.
Doc drops his lantern, causing the other dwarfs to pile up behind him, but it disappears when he and the other dwarfs reach the house after their work in the mine.
When Snow White first enters the dwarfs' house, the animals follow her in. Near the door, there is a rabbit and another rabbit walks beside it. As the second rabbit passes the first one (behind it), it changes into a brown squirrel.
At the end of "The Silly Song", there's a cutaway to Dopey playing the drums, yet he's standing atop Sneezy during the song/dance at the same time.
The seat on the organ when Snow White arrives at the cottage is a bench. Later, when Snow White and the dwarfs are dancing and singing, the seat is no longer a bench.
The prologue tells us that the Queen put Snow White to work as a scullery maid, which explains why she is so handy with a broom, but does not explain how she knows how to make stew and pies. Scullery maids held the lowest-rank of the household staff. They might be called upon to perform cooking prep (scale fish or pluck fowl, etc.), but were never allowed to prepare meals.
The jewels that the dwarfs mine are diamonds, rubies, and other stones normally not found together. Also, the jewels are already faceted and polished.
During "Whistle While You Work", the raccoons are seen washing clothes in a river. Considering that detergent was not yet invented, the clothes would not have gotten any cleaner.
Bashful shoves the vase of goldenrod into Sneezy's face, triggering Sneezy's hay-fever. Goldenrod does not cause hay-fever; however, frequent handling of goldenrod can cause allergic reactions.
When the seven dwarfs are done for the day, they give Dopey the key and he locks up and then hangs the key on a door-nail before heading home. The diamonds could easily have been stolen if the key was left on display. It would have been better if Dopey took the key with him rather than hang it on a door-nail for robbers to see and steal the diamonds in the vault. This oversight was most likely intentional as part of his character.
Grumpy is seen playing a piano. Pianos were not invented until the 1600s and this film is set in roughly the 13th century. However, what Grumpy is seen playing is not a piano at all, but an elaborate pipe-organ.
Even though the dwarfs apart from Dopey are either middle aged or elderly, Bashful looks too young to have a white beard. Judging by his appearance, Bashful looks as if he is in his mid forties. Male humans don't have white hair till their fifties at least. However, some humans do have prematurely grey hair by their early forties due to a number of factors.
In the last scene, the Prince shimmies. The cels were not lined up correctly when the scene was shot, and his body shakes. Walt Disney was horrified when he saw the mistake in the color dailies, and wanted it corrected. No money was available to make the correction because the film was already far over budget, so Walt's brother and business partner, Roy O. Disney, declared, "Let the Prince shimmy!" and so he did - until 1993, when the mistake was corrected during Disney's digital restoration of the film.
When Doc removes the bed cover from Snow White while she is sleeping on the dwarfs' beds, for a few frames we can clearly see artists' mistakes of an outline of Doc's hand having been drawn in the wrong place for the frames.
When the dwarfs are coming out of the tunnel after work to sing "Heigh Ho," Grumpy and Happy suddenly appear.
During Snow White's vigil, when Bashful, Sneezy, and Sleepy are shown crying, one of Bashful's eyebrows disappears for an instant.
During the washing song, six of the dwarfs circle around Grumpy before they ambush him. But when the dwarfs disperse to carry Grumpy, Dopey has disappeared, but reappears to help Sneezy get Grumpy in the tub.
When Snow White and the animals are walking up the stairs of the Dwarfs' home, the wide shot of the stairs hangs on the last cel of the animation for a few extra frames before cutting to the close-up of the turtle, leading to a somewhat awkward shot transition.
The Dwarfs' house has a water hand pump in the kitchen. Hand pumps were a communal device used by villagers to access water from an underground well. That the Dwarfs have a pump indicates that either the house was built over a well (unlikely as a creek runs in front of the house) or the Dwarfs have indoor plumbing (even less likely as the Dwarfs use the trough outside to wash up for dinner). We have to assume the pump was included by the animators without thinking it through as "Whistle While You Work" is set partially in the kitchen.
In this story set in the Middle Ages, Doc is depicted wearing glasses of the type that Benjamin Franklin would wear in the 18th century. Glasses were invented during the Italian Renaissance but weren't sold until 1466.
Both Snow White and her stepmother in her Queen form are seen wearing pump shoes, but as this film takes place in medieval Europe pumps would not have been invented in this period of time.
We see clocks at both the mine and the cottage, but there were no clocks in the Middle Ages. In those days people measured time by observing sunrise and sunset.
Snow White wears the popular hairstyle of the time the film was made.
When Bashful shoves the goldenrod into Sneezy's face, Sneezy yells at Bashful angrily "My hay fever!" as the flowers trigger his sneezing. While people undoubtedly suffered from allergic rhinitis in Sneezy's time, it wasn't diagnosed as "hay fever" until the 19th century.
When Snow White is kissing all the dwarfs' foreheads, before she kisses Dopey, we hear her say "Oh, Dopey!", but her lips never move.
When Snow White gets up to dance, Happy is playing the bass, but no sound comes out.
Snow White presumably takes place in medieval/pre-industrial Europe, specifically Germany. However, some of Snow White's animal friends are North American fauna: chipmunks and raccoons. The latter were introduced to continental Europe in the 1930s.
Daffodils are native to southern Europe and North Africa, but did not become popular in the rest of Europe until after the 16th century.
Doc admits to Snow White that none of the Dwarfs have washed in ages, yet when she tells them that they must wash up before she'll let them eat dinner, there are bars of soap waiting for them at the trough.
The Prince shows up at the wishing well to court Snow White, without any explanation as to who he is or how he got there.
When Snow White took refuge in the forest and the evil queen found out, why didn't she send out her castle guards' search party to look for Snow White? Also, why didn't the queen have her castle guards protecting her as she's seeking to kill Snow White?
When Doc is assaying the (already cut) gemstones from the mine, he puts the jeweler's loupe into his eye backwards.
At the final scene when Snow White kisses the dwarfs, she kisses them all except for Sleepy.
As Snow White kisses each of the dwarfs as they leave for work, Happy is the only dwarf who doesn't get kissed, and is bizarrely nowhere to be seen at all.
Snow White decides to take a nap, despite the fact that she left food cooking and table candles lit. A deleted scene shows her slowly realizing her mistake and rushing down to the boiling pot of soup to cool it.
Grumpy slams the door behind him as he and the other dwarfs march outside to wash for supper. Minutes later, Snow White calls them for supper, but no one would have heard her through a closed door.