This tab hasn't been updated since 1996, so I think it's about time. I don't think the chords are correct. The first few lines of the verse are really just a C-C7-F-F7 progression played like this (I don't know how to do the tab, so I'm going to have to do it the hard way):
1) Make a partial barre with you index finger at the 8th fret, with your middle finger on the 3rd string, 9th fret and your ring finger on the 4th string, 10th fret. You'll recognize that this is a partial "E Form" C chord. Strum this twice.
2) Kept your hand where it is, but lift you ring finger off the 4th string, 10th fret. You now playing a partical C7 chord. Play this twice as well.
3) Now play an "E form" chord, at the 7th fret, only one string up. In other words, your middle finger should be on the 6th string, 8th fret; your ring finger should be on the 5fth string, 8th fret; and your index finger on the fourth string, 7th fret. You'll recognize this as actually the very top of a "C-form" F chord. Play this twice.
4) Leaving your other two fingers where they are, move your ring finger to the 3rd string, 8th fret (you will want to dampen the 5th string, which is now open, with your middle finger, which is fretting the 6th string right above it). Play this twice.
If you know the song, the rhythm of the strumming should be easy to figure. If you want to play the intro, that's easy. With your index finger on the 3rd string, 12th fret and your middle finger on the 1st string, 12th fret. You'll recognize this as "D form" C chord at the 12th fret, without your ring finger on the 2nd string, 13th fret. Slide into the figure, at the 12th fret, and play it twice. Move it down a fret and play it once. Move it down to the 1oth fret and play it again. Then play the chords to the verse. You should be able to fool around with it to get the rest of the intro, or something very close to the record. Don't worry about getting it exactly the same. Garcia didn't.
As for the rest of the verse, I think the tab is correct, although I'd add the G7 and A7 also. For soloing, just play off the major pentatonic scales for each chord, emphasizing the the 7th on the C7 and F7 at the chord change.
Anyway, that's my take on Alligator