There were a number of issues here that probably don't cause a no-permission message but I will enumerate them anyway.
1. AJAX Quick Reply did not work in XenForo for wiki comments. It would only post comments if AJAX or quick reply was disabled, or if the user clicked "More Options" before submitting.
2. Navigation links for multiple pages of a discussion that was not the main discussion were wrong.
These are fixed in the next release as some of the fixes for number 1 involved adding new files and editing many existing ones.
If you see the "More Options" link, please click that before trying to post. It may provide more information. If you are not testing using an admin account, please do. There may be database errors or other problems that are hidden to non-privileged users.
In the XenForo CP, go to Tools > Logs > Server Error Log, and check if any new entries appear when you try to make a comment.