Possessive pronouns - Zaimki posesywne

In response to Jim's question about the possessive pronouns in Polish:

Pronoun swój, swoja, swoje // swoi, swoje indicates possession and can be interchanged with the possessive mój, moja, moje // moi, moje. However, there are certain contexts in which this exchange is either gramatically incorrect or it just doesn’t sound right (I know, lots of things don’t sound right in Polish, and there’s no rule telling us how to avoid the embarrassment of not sounding right...). Oh well, one thing’s sure: people will understand what you say even if you mix these pronouns up once in a while – and they will be kind enough to correct you without making you feel odd for not catching the subtleties of the language. But that’s just not good enough, is it? So here’s my best attempt at making things clearer – I have my reasons (mam swoje powody) to believe that this is one of the trickiest parts of Polish grammar: usage of possessive pronouns.