some of us Poles have problems with pronouncing trilled R's
This is called 'speech impediment'. Speech impediments are quite common (but not that common), so everyone in Poland has had at least several occasions to hear Polish people with the impediment re trilled 'r'.
On the other hand, I wonder what kind of speech impediment Jarosław Kaczyński has when pronouncing the -ą ending improperly. In most cases he says -om rather than -ą. Any thoughts?