In the first screenshot you notice that I can't build the "Globe Theater" even though it indicates that I've 1 left. So I check that in a nearby city (screenshot 2) and their it checks out, having 1 remaining item to build should allow to actually start building it. A few turns later .... screenshot 3, it has magicly turned to 0, without building any global or national wonder. Now isn't that strange ?

In ss 1, you cannot build the Globe Theatre because you have not built a theatre in the city. (Pavillion since you're playing as Chinese).

In ss 3, you have built the required Pavillion but you cannot build the Globe Theatre because it is already under construction in another city - that's why it says 0 left.

Correct me if I'm wrong, but this is not a bug. These sort of posts really shouldn't end up in the Bug Reports forum. The Quick Answers thread would be more appropriate.