Something that constantly grinds my gears is (main) characters being anti-slavery while the slave trade is up and running in the historical context. I assure you: most people were pro-slave or didn’t care. Being anti-slavery was an extreme political opinion and wouldn’t be considered small talk.

Teeth.

American period films almost always have the main characters with super-white gnashers.

Mel Gibson in The Patriot. Guy wasn't even born until almost 200 years later.

One I'm starting to notice become more popular due to the current culture in Hollywood; actors with obvious plastic surgery in historical settings. It's like a continuous anachronism throughout the movie constantly breaking the fourth wall.

Nothing is ever colourful in movies set pre-renaissance, everyone looks like a pauper and kings dress in fucking black leather armor..

In reality most people these days would probably be slightly upset by how garish things were back then, everyone LOVED colour! Even the poorest people would probably have access to some shittily dyed red clothing at least, and from there up the social ladder it would just get more riotously colourful until you get to the nobility who dressed like absolute dickheads.
The Witcher 3 is actually a pretty good way to get a basic idea of what the past was like: not accurate to any one period or region (and mostly draws from renaissance-y europe), but if you ignore the fantasy bits it's generally closer to sensible than not, and certainly vastly better than most modern portrayals..

Here's some at least reasonably representative images in order of increasing social status, not necessarily from the same places but all from roughly "medieval" times:

Bonus:

Dropping my favorite history/movie youtuber, History Buffs. He does a great job of dissecting movies for historical accuracy in an entertaining way.

Here he is sad (Braveheart):

https://www.youtube.com/watch?v=ojBwASARAzo

and here he is happy (Master and Commander):

https://www.youtube.com/watch?v=_Iwea41ua0Y

A Knight's Tale has a lot of very deliberate and very obvious anachronisms in it. But I don't feel like they detract from the story. It felt a little out of place, but at the same time, it felt more immersive.

That, and Heath Ledger was brilliant and Alan Tudyk was hilarious.

There was a little movie about the 18th century baroque composer Vivaldi. From my memory (like 20 years ago) it showed him using a modern violin bow. And the music played was from recordings using modern instruments. My area of expertise is early music so it pissed me off.

I saw a play about ancient Rome by an up and coming British playwright and one if the scenes had a clock in it.

Most westerns use that same patch of ground in Hollywood that has a vehicular track used by the film truck.

I could barely withstand the latest Wuthering Heights with Margot Robbie. Usually anachronistic music, sets or wardrobe doesn't bother me. Most of the times it is tastefully done or are details that are immaterial to the experience. But lord, this version was so over the top that I sometimes felt like I was watching a fashion show and not a movie. I'm still somewhat warm towards Emerald Fennel, but this movie was a let down for me mainly for that one reason. She is also pretty gross and can't help but to always include disturbing imagery, even if the script is supposed to be a romantic tragedy. Some of the scenes didn't subtract anything, but definitely added nothing as well. I think this film failed at what Marie Antoinette (2006) succeeded.

I notice wardrobe and the underwear in Dirty Dancing always bothered me, it looked too modern.