Hi Piotr,
Just to confirm, did you download and setup the .po file or the .mo file? It is the second of those that WordPress actually understands.
The Events Calendar itself also ships with translations, including a Polish translation and – just as with Events Calendar PRO – you can grab the latest files from translations.theeventscalendar.com.
One other thing to bear in mind is that, following recent updates, some pieces of text may not yet have been translated or may be in need of an update, in which case you are welcome to help out and submit new translations 🙂
Does that help?