Ahoy!
Well, like you said, Dylan's missed out on some greats but that's his loss! All of the music I love most has been made in the past twenty years! Props to your mum, though - it's good that she's kept an open mind (unlike Dylan!). I wouldn't be surprised if he was just being controversial to get in the news - I notice that he's got a new album out which obviously needs publicising!
That's true about Bowie and Johnny Cash also John Peel was knocking on a bit (60 ish?) but they all liked modern stuff - Cash even covered a Nine Inch Nails song! Like you said, when Dylan dismisses modern music, he's the one that misses out!
Thanks,
Corporate_Automaton