If I were to do the JMT over again, I'd take 21 days (or more - maybe even 4 weeks) so as to have time to (re)visit some of the really extraordinary places that are *just* offtrail. (If you hurry too much, you have no time for any of these places!)
Yosemite section: Half Dome or Clouds Rest
Tuolumne to Reds Meadow section: Ediza Lake and/or Minaret Lake. (In fact, I'd just leave the JMT at Ediza, climb the class-2 rock over to Minaret Lake, and hike from Minaret Lake back down to the JMT). Also, I'd like to check out Davis Lakes or some of the other stuff near Donahue Pass. Also, the world's most stunning meadow is west of Garnet Lake; you can leave the JMT at the northeast end of Thousand Island Lake, walk the lake to its east side, jump over the little pass to the Garnet Lake basin, and revel in the meadows/lakelets up there before following the north side of Garnet Lake back to the PCT.
Reds to Lake Edison: Duck Lake. I'd also like to explore the Silver Pass area; lots of lakes, and it's absolutely stunning there.
Edison to Mather Pass: Darwin Basin. Ionian Basin. Ladder Lake.
Mather Pass: Diversion to climb Split Mountain (a 14-er).
Mather Pass to Pinchot Pass: Bench Lake. Maybe the upper part of the Muro Blanco or the areas just to the north of that.
Rae Lakes area: Dragon Lake and Sixty Lakes Basin are just freaking gorgeous. Very quick to get to. Worth a very long stopover day to visit both. I've only been to the southern part of the Sixty Lakes Basin, but I'm told that the northern end (which comes to an abrupt dropoff) has a view to die for. In a very long day you can also hop over from Sixty Lakes Basin west into Gardiner Basin.
Kearsarge Pass: A very pretty, and (relatively) easy pass if you require a resupply exit from the JMT. Kearsarge Lakes are very scenic (though overused); Charlotte Lake is not scenic.
Forrester Pass to Whitney area: Diversion to either Lake South America area, and/or Wallace Lakes. Personally I don't find the JMT between Forrester and Whitney to be very interesting, so I'd do a diversion there for sure.
I did the JMT in 1999, but to this day remember every single place I camped, all 21 days. It's that memorable.