Interesting. That is annoying when that happens. Has happened to me before as well.
Castling misclick protection?
In daily games, it asks you to confirm the move, but in live chess it doesn't. They should make that a setting.

In daily games, it asks you to confirm the move, but in live chess it doesn't. They should make that a setting.
It only asks in Daily if you have that configured. The option is also available for Live in the app, just not the website.

Mobile app is very limited in terms of functionality, there are many options (like conditional moves in daily games or being unable to tag puzzles) that are simply missing in the app. I wouldn't advise to use it, if you want to fully enjoy and experience certain aspects of this website.

There should be a confirm castle move. Can't tell how often I accidentally castle. Maybe have the boxes turn red?

Move confirmation does not work for fast disciplines. However castling should be optional as an exception.
I know of a website that has some kind of castling confirmation. Green Chess website.
In addition to this: there should be some castling setting that clarifies what your controls are for castling. I personally generally castle by first touching the king and then the either of the squares 2 places besides him. But the app also recognises touching king and then rook as castling.
Ugh I was trying to start a new paragraph. But apparently enter = send and not new line. Ffs. Anyway, the reason that what I previously described is a problem is that I often select some pieces when I'm thinking of my move. This is rarely a problem, but it is a problem here, because it'll happen that I select my king and then decide I wanna move my rook. Instead of being allowed to move my rook like I want to, it'll then castle for me, which is really annoying. On other chess sites doing this doesn't lead to castling btw.
It's not extremely often that it happens, but sometimes you try to castle, and you misclick on (or drag onto) the wrong square, and the king ends up moving to f1 (or f8) instead of castling. This pretty much ruins the game, especially since there are no takesy backsies at chess.com. This is also pretty much exclusive to chess.com (and possibly to other similar online chess sites) and doesn't happen in real-life games.
So I was thinking if there could be an option you could turn on to protect against this. It would work as follows:
If both Kf1 (or Kf8) and O-O are valid moves, and the player moves Kf1 (or Kf8), some kind of confirmation popup, or other type of interactive element, would appear to ask if you are completely sure you want to do that. Maybe here you could choose between the two moves, or cancel the move attempt altogether. Obviously if the player plays O-O directly it can be assumed it's not a mistake and thus in this case nothing is asked. The same protection would apply to long castling as well, of course.
This protection would be optional, turnable on or off in the settings.