When trying to post a public message after having sent an private one before, won't be sent, even if you're still able to type in a message.
This is true for an first attempt or any thereafter.
Messages in the private chat still work as usual, the company chat I've not tested.
Closing the chat window and reopening it is necessary for sending public messages again.
Edit: Before switching back to public chat, it helps to set the privat chat selector on 'show all'.