Previosu ideas I have agreed with:
What I Got - Sublime
Sunshine of your love - Cream
anything by Nirvana or Talking Heads, esp. TH considering Bobby had already brought Take Me To The River to the table. Other TH's covers I could see the Dead do:
And She Was
Burning Down The House
Once In A Lifetime
What A Day That Was
Life During Wartime
(Jer or Bob..maybe everyone, ala Maggie's Farm?)
would've been remarkable. Can you picture the Dead doing any of those awesome TH songs? Sweeeeeet!
But I also think the natural graviation to some Phish cover would've been bound to happen. Maybe:
Bouncing 'Round The Room
My Sweet One
(a slowwwwwed down version, though...we all saw what happened to Bob when he joined Phish @ Shoreline)
Get Back On The Train
(Jer or Bob)
Sample In A Jar
(Jer...what an awesome encore this would've been at a Dead show!)
As for other bands, probably more Beatles and Dylan, as someone else stated, as well as a few more tunes from the Rolling Stones.
Also....maybe Hook or Run Around by Blues Traveler w/ Jerry singing it? I can hear him whaling on the solo, making it sound like John Popper's harmonica! Yeah!