Thérèse's ahistorical shaved underarms
In Secret strikes me--untrained though my eye is--as incorporating a more or less scrupulous re-creation of mid-nineteenth-century French clothing, buildings, common objects, and lifestyles. One error that I did notice, however, and that annoyed me quite a bit, was the absurd, more or less clean-shaven appearance of Thérèse's armpits. Underarm shaving was almost unknown in nineteenth-century Europe--as is evidenced, for example, by the anonymous nineteenth-century sexual memoir My Secret Life, in which the author, recounting his sexual encounters with hundreds of women (including prostitutes) all over Europe, often expresses admiration for women's armpit hair but never once, as far as I know, mentions a woman's armpits being shaved. I suppose that at certain times and in certain places, some relatively prosperous women might've temporarily shaven themselves in preparation for wearing a sleeveless dress at a social event, but that's the only significant exception I can think of. And I suspect that for women to shave their underarms to please a husband or lover, at his request or otherwise, was vanishingly rare.
The reason for this error might have been ignorance, a belief that it was an acceptable poetic license, a desire to protect the moviegoing public from the presumedly upsetting sight of female armpit hair, vanity on the part of actress Elizabeth Olsen, or a combination of these. I don't consider any of those reasons to be acceptable, though.