Since this thread has been resurrected, I might as well add my input.
But why is it that Poles understand Slovak and Ukrainian much better as Czech? Slovak I could understand, being a West-Slavonic language. But Ukrainian, being an Eastern Slavonic language. Strangely I have to admit that I through my (far from perfect) Polish also understand Slovak and Ukrainian quite well. There has to be an explanation for that.
Slovak vocabulary is very close to Czech and it writes words in a very similar manner, but pronounces them a lot more like Polish. For example, "teplo" means "warm" in both Czech and Slovak. Czech pronounces "teplo" as "teplo", but in Slovak, it sounds like "tieplo" or "cieplo," which is very similar to Polish "ciepło."
Even though Ukrainian is an East Slavic language, Polish and Ukrainian share a lot of common vocabulary as a result of borrowing. East Slavic verb conjugation patterns are quite easy to understand, and even though it forms the past tense the East Slavic way (e.g. "my byli" (Russian) vs "byliśmy" (Polish) vs "byli jsme" (Czech)), this East Slavic feature has permeated many Polish dialects, and is easy to understand whether you're familiar with it or not. Ukrainian has also adopted some West Slavic grammatical features, such as using "ja maju" ("I have", "mam") instead of "u mienia jesć" (Russian).
So even though Czech and Polish have very similar vocabulary, they have diverged too far in pronunciation for easy intelligibility. And even though Ukrainian and Polish are from different branches of the Slavic family, they have converged in terms of grammar and vocabulary, most likely due to shared history.