  We show that $m$ points and $n$ two-dimensional algebraic surfaces in
$\mathbb{R}^4$ can have at most
$O(m^{\frac{k}{2k-1}}n^{\frac{2k-2}{2k-1}}+m+n)$ incidences, provided that the
algebraic surfaces behave like pseudoflats with $k$ degrees of freedom, and
that $m\leq n^{\frac{2k+2}{3k}}$. As a special case, we obtain a
Szemer\'edi-Trotter type theorem for 2--planes in $\mathbb{R}^4$, provided
$m\leq n$ and the planes intersect transversely. As a further special case, we
obtain a Szemer\'edi-Trotter type theorem for complex lines in $\mathbb{C}^2$
with no restrictions on $m$ and $n$ (this theorem was originally proved by
T\'oth using a different method). As a third special case, we obtain a
Szemer\'edi-Trotter type theorem for complex unit circles in $\mathbb{C}^2$. We
obtain our results by combining several tools, including a two-level analogue
of the discrete polynomial partitioning theorem and the crossing lemma.
