Update from Blizzard on US forums :
Hi folks, while the above issue was reported to be resolved as Boubou mentioned above in the old thread, we’re seeing some sporadic ongoing issues, so the problem is being looked into further.
I’ve split the thread to create a new one to track the current problem.
Some players have reported that performing general troubleshooting steps corrected their issue:
@Rejuvithorn, TY for creating this topic.
There is also a case (Europe player) on the US forums:
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That’s what prompted this thread 
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Well, why did it take som1 posting on the US forum to get a response in the EU forum after all the posts about the issue. ??
There’s several issues, some have been corrected, some not. I agree it’s getting a little confusing due to older (and some VERY OLD) threads getting mixed up with the newer ones. We’ll clean it up a bit.
Had a problem a few days ago with that error 39500 and with 300016, and I solved it. Problem is, a lot of people on Battlnet in settings put that when they enter into game to leave Battlnet,I had that option too, I changed when I enter in-game, to keep my Battlnet online and didn’t had anymore problem with that error in Diablo 3,hope this can fix problem to others players.
Had a problem a few days ago with that error 39500 and with 300016, and I solved it. Problem is, a lot of people on Battlnet in settings put that when they enter into game to leave Battlnet,I had that option too, I changed when I enter in-game, to keep my Battlnet online
Same issue here - can’t connect same error message
Hello folks,
If you’re experiencing 39500 or 300016 please long into account management and change your password:
https://account.blizzard.com/security
Once done, try logging into the battlenet app again, and then Diablo 3.
Please report success/failure in this correction.
Okay, thank you. While it sounds odd, please try changing your password, but change it to exactly 16 characters long.
After years away from gaming I thought Id fire up Diablo 3 today… seems Blizz still dosnt run right after all those years.
D3 downloaded, Error code 300016. changed password, still not working, changed it to 16 chars, still no…
Want players to return? fix this please. Otherwise it will be another 5 years before I bother to try and log in again.
Edit: same thing happening on wife’s account
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Awesome support… thanks for ignoring. bye.
I change my password game is now work but I played maybe 3-5 minutes and error code 1016 disconnected me so I log out and log in and this error code in an instant jump on me every time so what to do next
300016 error still occuring. Europe server.
same here
if i change region to americas it works
Hello! Could you try logging in now please and let us know if it’s okay for you? Thank you folks 
[edit] To be clear, the problem should be resolved now, and a password reset shouldn’t be needed.
I had the same problem. Changing to a 16-character password indeed solved it for me. As an IT-professional though, I have to say that’s a very strange solution. But oh well, I guess as a method to get people to choose long passwords, it certainly works 