There are at least two iterations of They Love Each Other: the fast version and the mid-tempo version. The fast version was featured in these pages a while back (link at the bottom of the page), so the time is ripe for a complementary foray into the mid-tempo version.
One thing I’ve been listening for on They Love Each Other for a while now is extra emphasis put on the little riff that leads into the chorus. There was a Dead cover band in Chicago called Paradise Waits and when they played They Love Each Other they really emphasized that little riff. I thought it was such a great little nuance to the song. I don’t know if they gleaned it from the Dead or the JGB at some point or if it was something they came up with, but I always liked it. (Check out an example here. c. 1:45 and 2:45, for instance.) I never asked the guys where that particular part of the arrangement originated, but if you know of any Dead/JGB versions that are similar I’d be interested to know which ones.