With hindsight, this record actually begins to make a little sense. It's still pretty awful; it wouldn't be the record I'd play anyone to prove why Dylan's live recordings matter. Of all the live recordings, only Bob Dylan At Budokan
This is the genesis of everything Dylan has done since. It's a dry run for The Never-Ending Tour. If you've been to a Dylan concert in the last five-to-ten years, he sounds much like he does on Dylan and the Dead, only his vocals are far more confident, and his backing band sounds like they may have rehearsed the songs before trying to play them.
Dylan's voice had been in decline since the 1974-1976 peak of Blood on the Tracks through the Rolling Thunder Revue to Hard Rain. By 1985's Empire Burlesque, he's completely lost confidence in it, and what you get is an album of mailed-in vocals, buried under screaming female backup singers (bad idea, Bob) and synthesizers and synth drums and various other crap no one wants to hear on a Bob Dylan record.
On Dylan and the Dead, that's pretty much the order of business, except there's nowhere for him to hide how lousy his voice has become. What happens around 1989's Oh Mercy is that Dylan finally decides to adapt to, and run with, what he's got left. The phrasing becomes sharp again, and his command over the proceedings returns. Once, in 2001 or so, I saw him sing an entire verse of A Hard Rain's A-Gonna Fall in Woody Guthrie's voice. He couldn't have done that in 1987.
The song selection, as pedrolio mentions, borders on being ridiculous. I believe Dylan picked the songs himself, which could only mean he didn't want anyone to like it, or even buy it from reading the back cover. Out of only seven songs, you get two from his widely loathed-and-misunderstood God rock phase, two that are completely obligatory, and Joey, which may be the worst song he ever wrote (anyway it's right up there with No Time to Think). Only I Want You and Queen Jane Approximately are really suited to the Grateful Dead's style, and these are the songs which work best, done as the hippie shuffles with chiming guitar that the Dead do so well.
The version of All Along the Watchtower is also worthy of mention. After running through the chords a few times, Jerry unleashes a screaming solo at the exact moment Bob begins to sing. Jerry sort of trails off in embarrassment and waits for the end of the verse. You think they rehearsed that one at all? Even though there isn't much to recommend this beyond its bad-humor value (and Jerry Garcia shouldn't try to sound like Jimi Hendrix), Dylan copped this arrangement for his Never Ending Tour, and has been using it ever since.
Another interesting note-- it's rumored that a couple of years later, 1990 or so, Bob Dylan asked Jerry if he could join the Grateful Dead. They put it to a vote, and the vote came back "no". It's probably a good thing that never happened, but there are more connections between Dylan and the Dead than fans of either are willing to acknowledge, like the way Dylan sometimes sounds like he's fronting the Jerry Garcia Band these days.