The cheerful tempo of this performance doesn't fit well with the the message. Try a different version, because the Dead has done some very good versions of this song. It's one of their best Dylan songs.
The Dead does Dylan so well, but I think Dylan's own recording on "Blond on Blond" made in Nashville with Robbie Robertson and Al Kooper captures the nighttime slightly depressed, slightly paranoid feeling with remarkable finesse.
Visions of Johanna may be the Dylan song that the Dead interprets best.