Quick-change is just the easiest way to replicate it, it actually happens in a lot of random situations under normal usage.
Basically, the NPC will start rapidly twitching, constantly trying to load a skin but being entirely unable to. This is a visible twitch that's disruptive to gameplay, not to mention never loading a skin or showing equipment.
Using Citizens # 1166, the debug output looks like this:
[Citizens] Using cached skin texture for NPC bob UUID e7dbbf47-7c84-40e5-ba91-c9f6e6791306
[Citizens] Using cached skin texture for NPC bob UUID e7dbbf47-7c84-40e5-ba91-c9f6e6791306
[Citizens] Using cached skin texture for NPC bob UUID e7dbbf47-7c84-40e5-ba91-c9f6e6791306
[Citizens] Using cached skin texture for NPC bob UUID e7dbbf47-7c84-40e5-ba91-c9f6e6791306
over and over, on loop, twice a second, perfectly corresponding with the twitch.
Using the debug output in #37 , the debug looks like this:
[Citizens] Reloading skin for 173
[Citizens] UpdateSkin called for 173
[Citizens] Delaying skin load for 173
[Citizens] Using cached skin for 173
[Citizens] Reloading skin for 173
[Citizens] UpdateSkin called for 173
[Citizens] Delaying skin load for 173
[Citizens] Using cached skin for 173
[Citizens] Reloading skin for 173
[Citizens] UpdateSkin called for 173
[Citizens] Delaying skin load for 173
[Citizens] Using cached skin for 173
[Citizens] Reloading skin for 173
[Citizens] UpdateSkin called for 173
[Citizens] Delaying skin load for 173
Two batches per second again.
Here's a video demonstration of how to replicate the issue, also showing the issue up close:
https://www.youtube.com/watch?v=lOhxek04v7U&feature=youtu.be
(Ignore the skins not showing in the beginning, I'm on a 1.7.2 client, it's irrelevant to the issue, which has been confirmed on multiple client and server versions by other users)