  An improper interval (edge) coloring of a graph $G$ is an assignment of
colors to the edges of $G$ satisfying the condition that, for every vertex $v
\in V(G)$, the set of colors assigned to the edges incident with $v$ forms an
integral interval. An interval coloring is $k$-improper if at most $k$ edges
with the same color all share a common endpoint. The minimum integer $k$ such
that there exists a $k$-improper interval coloring of the graph $G$ is the
interval coloring impropriety of $G$, denoted by $\mu_{int}(G)$. In this paper,
we provide a construction of an interval coloring of a subclass of complete
multipartite graphs. This provides additional evidence to the conjecture by
Casselgren and Petrosyan that $\mu_{int}(G)\leq 2$ for all complete
multipartite graphs $G$. Additionally, we determine improved upper bounds on
the interval coloring impropriety of several classes of graphs, namely 2-trees,
iterated triangulations, and outerplanar graphs. Finally, we investigate the
interval coloring impropriety of the corona product of two graphs, $G\odot H$.
