The use of infinitesimals in calculus! Things like integrating against "dx" or taking a derivative of a function "df/dx" make calculus seem like something it's not. Worse, it really introduces a whole new language whose rules for manipulation are unclear.

Like if we have a function f(x,y), we often write the "total" derivative of f as df = (df/dx) dx + (df/dy) dy And the rules for manipulating a differential like this are quite strange (e.g., dx on top cannot cancel the dx on bottom).

There's a language of differential forms that makes this notation a bit more rigorous, but I still think the notation is very misleading and confusing, especially for those who begin to learn calculus.