Rips in Alice's lace dress at the elbows appear and disappear in the early part of the film (before going down the rabbit hole).
The film very clearly states it is supposed to be 1905, yet the car ride is taking place on a modern American road. Note especially the presence of a painted center line (those didn't exist until 1911), and a modern American two directional arrow sign. By the way, the yellow center line and white edge line scheme ubiquitous today was not standard until the 1971 Manual on Uniform Traffic Control Devices; many streets before that either used all one color or had yellow and white switched.
When Alice has a flashback to her as a younger child with her mother, the actress playing young Alice obviously has modern nail polish on her nails. While coloring nails is thousands of years old (it dates back at least to 3000BC China), nail varnish or nail lacquer only dates to 1916. Before that, nails were "polished" in the same sense as you can "polish" silver-meaning to buff until shiny. (That is actually where nail polish gets its name.) The coloring generally came from using some sort of stain, and was done in a separate step from the buffing. When the first modern nail lacquers came out in 1916, it was a clear lacquer meant to save people the time spent buffing their nails to a shine. The first colored nail lacquer came out in the 1920s. Red nail polish, like that worn by the actress, did not come into vogue until Rita Hayworth in the 1940s.
Alice's older sister refers to "movies." This term was shortened from "moving pictures," and not used until 1912 (though some etymologists debate it was used rarely as early as 1908). Since this is supposed to be 1905, she should have referred to "moving pictures" or a "photoplay."
When Alice is woken up and dressed, multiple crew members are visible in the mirror in multiple shots. This is even despite a rather obvious CGI filter being put over part of one scene.