I'm going to categories the problems people may meet with information I know about. Hope which is going to help you or people with the same problems.
If you need any information, you may leave a comment by the facebook plugin. Or if you have any helpful information would be able to share with everyone, that'll be grateful.
When Can I Find An Appointment?
It mostly depends. The official says there're released at around 9 a.m. and 14:30. My watch data says they're mostly true but not always.
I put a heat map of when would people look for appointments on the home page. The map says that most of the time people are not seeing valid appointments. Now I'm working on to collect more data to see when they usually release appointments. This may help people to avoid more unnecessary checking.