  Let $FI(X,K)$ be the finitary incidence algebra of a poset $X$ over a field
$K$. In this short note we establish when $FI(X,K)$ satisfies a polynomial
identity and when its group of units $\mathcal{U}(FI(X,K))$ satisfies a group
identity. The Lie derived length of $FI(X,K)$ and the derived length of
$\mathcal{U}(FI(X,K))$ are also determined.
