Here's 3 suggestion to improve the plugin.
1) When i Select the HOUR for the appointment, and the confirmation box appear, the selected box of this time shoud have a different color. Add a Class="active" status to this box and in the css we can change the color of this active selected box. (better UX design).
2) Add a "Confirm / Reject" appointment action.
I'd would like to have the possibility to reject an appointment even though it's a paid one. That way I could cover a few situations where the provider had a problem and the admin needed to cancel it. There are a few other things that this feature could cover, specially in the transition from a paper schedule to an online schedule.
3) Add a button "proceed to confirmation" that SHOULD be clicked to make the confirmation box appear. That would also be an on/off option in the settings. This way the user can click in different hours before get the confirmation box displayed. I like the current setup that shows it automagically, but it would help the user not to lose himself in the middle of the process in some layouts.