Recently, we introduced a new automata model, so-called colored finite automata (CFAs) whose accepting states are multi-colored (i.e., not conventional black-and-white acceptance) in order to classify their input strings into two or more languages, and solved the specific complexity problems concerning color-unmixedness of nondeterministic CFA. That is, so-called UV, UP, and UE problems are shown to be NLOG-complete, P, and NP-complete, respectively. In this paper, we apply the concept of colored accepting mechanism to pushdown automata and show that the corresponding versions of the above-mentioned complexity problems are all undecidable. We also investigate the case of unambiguous pushdown automata and show that one of the problems turns out to be permanent true (the others remain undecidable).