We have the Appointment+ plugin running on a multisite install running about 20 sites. On all sites, but one http://homeishighpointe.com/tour/.
I did a bit of digging into the issue and tried to even create a new page with the shortcodes on it and I'm still seeing the styling issues. I found by inspecting the page, that the month view is being generated as a bunch of <td> tags. The problem is that all 31 days of the month are being put in between two <tr> tags, when there should only be 7 days at a time in between each <tr> tag.
My guess is that something is going wrong when the shortcodes are rendering the calendar view.
To answer the first round of questions, NO we cannot disable all plugins just to see if this is the issue. This is a live client site.