(It doesn't solve the problem of missing letters and missing diacritics when trying to write your language using English letters only — but Serbs, Ukrainians etc. can't write their language correctly using only Russian letters either.)
ś—sz
ć—cz
ź—rz/ż
dź—dż
Mandarin of all languages has this phonetic distinction, but I don't think any other Slavs kept the full set, on top of the nasals mjd wrote about.
I think these contrasts represent a very underacknowledged difficulty for English speakers learning Mandarin, because we're used to thinking of tones as the only hard thing. I'm still struggling to properly pronounce a friend's name that I think begins with /ʈ͡ʂʰ/. Maybe Polish speakers can deal with this easily!
Retroflex consonants are still awkward, but at least I can produce them reliably. What's really hard for me are uvulars, they feel a bit like choking every time.
They say:
"I pronounced the velar ejective consonant [k'] and all I got was this [t']-shirt."
There was a post on Language Hat or Language Log where a professor recounted meeting a student who had linguistics "as a hobby", which was astonishing to the professor -- and the student explained that this was possible nowadays because of Wikipedia. (To which I could add, for some people because of the conlang community, or because of linguistics blogs!)
Anyway, Wikipedia's coverage of linguistics topics is generally really excellent and detailed (maybe strongest in phonology, perhaps because of a few super-obsessed editors).
the point is I don't think Latin vs Cyrillic in Poland's case was driven by Polish language phonetics per se. I would venture to guess this had more to do with political/religious affiliations etc.