1. Given that $A$ and $B$ are both 672nd degree polynomials, and $C$ is a 671st degree polynomial, the degrees of $A+B$ and $A-C$ are $m$ and $n$ respectively. Then
$$
\begin{array}{l}
|m-n|+|2 m-n-672|+|-3 m-2| \\
=
\end{array}
$$
2. 2018.
From the problem, we know
$$
m \leqslant 672, n=672 \Rightarrow m \leqslant n \text {. }
$$

Then the original expression is
$$
\begin{aligned}
& =(n-m)-(2 m-n-672)-(-3 m-2) \\
= & 2 n+674=2018 .
\end{aligned}
$$