This happens a lot. A Pub gets a warning stating that the building does not contain any entertainment. I am assuming the beer is the entertainment (?). There is beer in the pub, and there are plenty of beer in the stores. So why does the pub complain about no entertainment?
I experience this a lot as well. I believe the problem is that pubs only have 1 worker (which is silly). So that one worker spends most of their time stocking the pub with supplies and not actually running the pub. They need to either add workers or give the pub an upgrade that does so.
personally never built one cos the drunkard rampage issue, but yeah kind of odd
You can have all the Beer in the Land, but if the Pubs have a Low stock of Beer this will happen.
Be sure to build a Storehouse nearby the Pub that allows the storage of Beer.
You can also set a Storage Limit on Beer in the Storehouse, so all the Beer doesn’t end up on just one side of town if you have more than one Pub. Doing this will help the Pub worker spend less time stocking and more time serving customers.
Hope this Helps! 
v.0.9.7e and sadly this is still the case.
Related to "No Entertainment" icon appearing incorrectly over Brewery & a Pub
Opening the pub, the entertainment meter at the bottom is full and says it is serving 39 of the needed 20 to be 100%. Beer has been plentiful (over 1000 in stock) and serving only one pub. The horn icon shows above it all the time all year long.
Edit, while watching this building more closely, the icon does go away periodically. I’m building a store house closer to set a storage quota for beer but the brewery is already pretty close. Perhaps the pub just needs a larger inventory stack size for beer. I just caught the brewer walking back to the pub with only 21 beer in hand, which is a problem I see with a lot of people only taking a tiny amount of goods even with baskets on their backs. It also appears that even with beer in stock and the action distributing beer in effect, the icon stays above the building likely until the end of the month.
Of course, it might also just be the case that a 1000 population town needs more than one pub. They’re just drinking too fast. So I’ll try that as well.
Edit 2: So this is strange. Upon opening a new pub, the worker went and picked up 50 beer, so I know they can hold more than 21. The first pub continues to refill with only 21 at a time, probably a figure derived by how much the pub had in stock when he begins his trip to pick up more beer. If they can carry that much, why don’t they just grab 50, refill the pub, and hold on to the rest until the pub sells some, then he can move more from his pockets to the pub inventory. Perhaps the market square needs to stock this item as well (it’s not currently listed) as any pub is going to need to be close to the housing for desirability buffs.
I’ve noticed this as well, and from what I’ve gathered, the icon shows when the worker is Shelter Stocking, or otherwise not in the building, or doing work-related stuff. So even when there is beer in the building etc, it also triggers when the worker is out of the building, and shows “No Entertainment Provided”.
Maybe there should be 2 pub employees. Effectively a barback for fetching more beer 