Online/busy/etc. are part of the core standards and very basic functionality. All software has occasional bugs, but I never encountered widespread issues with statuses such as you seem to be describing.

There was a period of time where if someone signed in using the Google+ chat client, they would appear online but wouldn't receive any messages you sent them from the XMPP side. That was entirely a Google implementation thing (they had stopped maintaining XMPP interoperability at that point).

The big growing pain for XMPP was behavior when you had multiple clients connected simultaneously. Extensions were added to the standard that unified behavior around which clients received messages (today we'd assume all of them but that was more up in the air at the time) and tracking of read status across clients in order to highlight new messages. But during perhaps the heyday of XMPP the extension was not universally supported by even some popular clients, so multi-client functionality could be confusing and inconsistent, e.g. messages delivered to only one client for no clear reason. This is a pretty well solved problem today but, well, no one is using XMPP.