iTunes, An unknown error occurred (502)

I appreciate your corroboration, but turning off the caching service doesn't solve the problem/mystery. You've worked around the problem by disabling a useful service that—for an unknown reason to us, but probably not to Apple—just punishes you, because now you won't benefit from the caching service. Perhaps you don't need it, and can happily re-download OS releases, patches, and apps for all your devices, but this service saves me *hours* of time weekly.

I agree with fact that Caching Service is quite important and in larger network environment essential. Mystery is still there and in my smaller controlled environment I will most likely switch it off every fortnight for as long as iTunes update get in and then switch it back on. On that note I wander if anyone has had same error on El Capitan and OSX Server 5.0.15. Thinking of dedicating this weekend to make a move to "latest and greatest".

Upgrading is, of course, exactly what Apple wants. However, their best intentions do not change the fact that sometimes computers need to remain static and we, as admins, need MUCH more transparency about how and why a service has suddenly decided to stop working so we have the knowledge we need to decide to use a stable, but unsupported system, or move ahead with buggier, but supported systems.

It is interesting to note that while enabled, the caching service's data size has incremented for Mac App Store downloads, but not for iTunes.

I had this error on my Iphone trying to download Google Maps. Turned off the Wi-fi and used the Cellular data instead and the problem went away. I would suspect the average home router has some ports blocked that Itunes tries to use on some downloads. Though I downloaded 2 other apps through the router with no problem.

Suggest trying different networks or go into your router setup and shut off all firewalls and enable all ports. That might fix your problem. And if Apple reads this i might suggest they look at these problem apps and see what they are doing differently from the rest and try a permanent fix at their end.