All great suggestions!
But remember that memory is also a function of biology and cognitive psychology. There are 3 main stages: Encoding, Storage and Retrieval.
To try to address this only by practicing an instrument or as it relates to music is still a very incomplete process.
There are memory competitions and champions. People have to remember the order of cards in multiple decks. Songs are easy by comparison.
Last year I read a book by Joshua Foer called 'Moonwalking with Einstein'. If you're really interested in improving your memory read this book.
And I disagree about drums being harder concerning memory. There are no wrong notes to hits. And if you hit tom 1 instead of tom 2,it doesn't change the song. Drummer don't have to worry about tonality at all. And everything that a drummer has to worry about(timing) applies to every other instrument. And if a drummer alters a beat but keeps time most people won't even know. But if we change the order of the notes to Brickhouse everyone will know. Try asking a drum what chord is on beat 3 of the 3rd measure and see what he says. Ask him what key the song is in. Ask him if he needs to remember that we're doing the Motown medley a whole step higher. He doesn't have to memorize any of those things. A drummer can fake a song easier than any other band member. I know, that doesn't have to do with memory. But he definitely has less concerns because there's always gonna' be a bass drum hit on beat one(generalizing).
peace,
anthony