1) In terms of sounds, John Frusiciante's guitar sound is about as modern as you'll get. Just about every part of the song has a different guitar sound, not so much from different guitars and amps as from effects. He goes from the dry out-of-phase Fender sound in the verse (sounds like a Jaguar or Mustang), to heavily reverbed with a slight delay in the chorus, to an auto filter in the second verse, distorted, modulated and so on.
2) This is not a perfect track in that you'll hear some slight timing inconsistencies. Not enough that you'd ever hear it with the rest of the instruments, but enough that an overzealous producer might feel compelled to cut and paste to straighten it out. It just goes to show that a track doesn't have to be perfect to work (although this one is pretty close). Same goes for the bass track in the second video.
3) In the second video, Flea's slap bass part is interesting in that it has to be compressed pretty hard to contain those slaps. Good engineering job here because a slap bass is one of the most difficult sounds to record and this one is smooth and even all the way through.
4) Note the ad lib bass punch-in at 3:15. You can tell it's an afterthought because the sound is different.
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