Interesting...I have had this problem all day with TextWrangler and Xcode and tried to figure it out. No luck though. This is new for me though...I haven't seen it before today.
By the way, searching a little, I did find this issue being reported to Apple and JAMF...
Apple's Discussion Page
Hey Joe,
We've currently got a ticket open with Apple about this. Looks like Device VPP for Macs, and User VPP for iPads, is down on their end.
We're encouraging all of our customers with an AppleCare agreement to contact Apple so that they can better gauge the impact. Please reference the following AppleCare ticket: 1163854473
Sorry for the inconvenience :(
-Matthew
We also have this problem. We tried free Mac Apps and Paid Mac Apps. Both result in the same error..
Had a talk with apple and they say everything is operational on their side.. So now I have opened a ticket with JAMF..
Thanks, Matthew.
I will call our Apple rep today and see what he has to say. I'm glad it's nothing I did!
rblass - What's your JAMF ticket number? If I need to call JAMF afterwards, I'd like to refer to it.
@joe.giguere
Hi Joe,
this is my ticket number: JAMF-0279728
Very much like to hear what they have to say...
Thank you. I'll keep you posted.
I think we have a similar issue, but the error has a different dialog box:

It only happens with (VPP) Mac App store apps (Microsoft Remote Desktop in our case, both all VPP apps fail). Checked items:
-all other policies work fine.
-We have a customised Self Service App
-jamf, version=9.92
-deleting this Self Service app, and running sudo jamf manage does not help.
-Clients on 10.11.3-10.11.5
-VPP token is still valid, no licence agreements waiting for agreement..
-Nothing in /var/log/jamf.log (which is normal for VPP app's I guess)
from ˜/Library/Logs/JAMF/JAMFApplications.log:
2016-06-30 9:25:50 AM <com.jamfsoftware.selfservice>: Error executing Mac App "Microsoft Remote Desktop"
Error Domain=JAMFSoftware/SelfService Code=20 "Quit and re-open XX App Store to try again." UserInfo={NSLocalizedDescription=Quit and re-open XX App Store to try again.}
with help from @mvdbent
Check out this post too, I guess the core issue is the same.
20411
Does it depends on user associated VPP Apps or Device based ?
We only use device based. So I have no knowledge wether it is also on User based ..
Hello.
We are seeing this exact same error when trying to install Final Cut Pro. We are using device assignment and the systems we are woking to install on are MDM compatible. I just wanted to chime in here.

No response at all from my TAM in 2 days. Tried emailing who I thought was our sales rep from a few years back but he's no longer there. Anyone know how I can find out who my sales rep is so I can get some attention?
No response here either.
I do notice a change in the message.
When the app tries to deployment no error is displayed but instead Credentials are asked for the app store.
@TomDay if you log into JAMF Nation and go the the menu at the top (menu with your JAMF Nation user name) and choose My Support then click the My Account Team tab it should show you who your TAM is. That assumes your JAMF Nation credentials are properly linked to your organizations account.
@mpermann thanks my TAM is there. Was hoping for my sales rep who I emailed and is no longer at Jamf . Finally heard break from my TAM 3 days later.
Hey all,
Just wanted to give an update to anyone waiting on VPP: Apple tells us the iPad issues are resolved, but the Mac issues still persist.
Same issue here. Tried it with macOS device assignment and Apple ID assignment. Theres no way to install OS X Server on that machine on device assignment.
Tried Apple ID assignment on Monday and ran into errors. Today i clears the App Store Cache (https://discussions.apple.com/thread/4362474?tstart=0) and tried to install it again trough the App Store. Finally successful.
But the device assignment error still persists.
Didn't realize this was still an issue. I ran into it today, reported to Apple. Not very confidence inspiring to see it's lingered this long.
My money is on this issue won't be fixed until MacOS Sierra drops.
I posted in a similar thread and I can't get OS X Server.app to drop on a few of my clients either. Tried clearing the cache and no dice.
two weeks now...
I sure hope Apple will not wait for the fix until Sierra because we (and lot's of other company's) have the problem now!
I agree @rblaas. Waiting is not the way to go here. There are a number of us that rely on this mechanism to work. When it isn't working, it creates problems for us. Additionally, we aren't moving to Sierra any time soon.
So let's get this fixed now, not later.
We are having the same issue here. Big issue for us because we have purchased an App that needs to be device based and the employee do some of their work without the App.
Tested this morning, still experiencing the same issues. Halfway through a ~400 device reimage using device assigned apps. :(
Will be logging a bug report with Apple to help reinforce urgency. Genuinely appalled that this isn't fixed when it is such a heavily used feature in enterprise and education.
I just asked Apple for an update. I received the following:
Thank you very much for your email.
I can confirm our Apple Engineers are currently working on the issue reported under Case ID 1163854473.
We don’t have an ETA for the fix from the Engineers, but if I hear anything I’ll let you know.
Have a nice weekend !
Kind Regards,
Imre
EDU Support
Apple Inc., on behalf of Apple Distribution International