What are the most common errors in math exams?

Errors in routine algebra, in particular problems with minus signs, often turn a very "doable" problem into one that the student cannot do. If this happens early enough in a problem, even partial credit can disappear.

The properties of logarithms and exponentials are often wrong. For example $\ln(xy)=\ln(x)+\ln(y)$, not $\ln(xy)=\ln(x)\ln(y)$. Not knowing $\sin$ and $\cos$ for the "special angles" like $0, \frac{\pi}{6}, \frac{7\pi}{4},$ etc.

Freshman's folly is all too common, $$(a+b)^n=a^n+b^n$$ for $|n|>1$. Although this does hold in finite fields...

My other two "favourites" are, $$\begin{align*}x^2-x&=0\\\Rightarrow x^2&=x\\\Rightarrow x&=1\end{align*}$$ and $$\begin{align*}x^2-4&=0\\\Rightarrow x^2&=4\\\Rightarrow x&=2\end{align*}$$