Compatibility with Vertical Tabs

On further inspection, I think it may have something to do with the vertical tabs module (http://drupal.org/project/vertical_tabs)?

Yes, the vertical tabs module causes the problem. After I disable the module the problem goes away.

This might be fixed by specifying the "minimum number of tabified fieldsets to show vertical tabs" setting to higher number or unchecking "include new fieldsets in vertical tabs by default" setting.

The only problem is when "Collapsed driven properties" is unchecked the fields render under the comment form. Also, when there is only one comment driven field, the fieldset title will not show at all.

When I enable more fields with "Collapsed driven properties" unchecked it renders the vertical tabs below the comment form. (see attached image).

Hope this helps

what is "Pothole Size" supposed to be? a comment driven property?
--Yes, I am trying to create a support ticket for pothole repair requests. "Pothole Size" is a comment driven property.

comparing screenshot at OP against the one at #3 I don't get the idea
"Driven Pot Hole Repair Request" vs "Changed Ticket Information" & "Publishing options"
--Sorry, after issue comment #1 I changed the "Fieldset Title" from "Driven Pot Hole Repair Request" to "Change Ticket Information" and added "Publishing options" as comment driven property

please, clarify what would be the expected result? (using a drawing perhaps)
--My expected result if using the vertical tabs module is:
--- to have all the comment driven properties inside a comment driven fieldset, some of the fieldsets within the comment driven fieldset will be vertical tabs. What happens now is the comment driven fieldset gets added as a vertical tab (see this)instead of surrounding everything - the "Collapsed driven properties" checkbox doesn't change this behavior it remains the same
--- to have the comment driven fieldset above the comment form, what happens now is comment driven stuff is below the comment form

you mention the option "Collapsed driven properties"
but, do you have selected "Display driven properties bellow comment form"?
--No, "Display driven properties bellow comment form" is unchecked

the fieldset is expected to be shown whether it is collapsed or not,
--Correct

also it should be collapsible for both cases
having vertical_tabs should introduce new JavaScript behaviors for such fieldsets, and it seems to me that the driven fieldset is not even getting a chance to appear at all, am I right?
--No, it appears but the fieldset now becomes a vertical tab (see this) Note: Change Ticket Information is the "Comment Driven Fieldset Title"

So, in summary there is two problems
1. when using vertical tabs module, comment driven properties appear below the comment form
2. when using vertical tabs module the "Comment driven fieldset" becomes a vertical tab instead of being a wrapping fieldset around all comment driven properties.

Hope that helps

Patch seems to work as expected. Vertical Tabs now work inside the Comment Driven Fieldset. Good Job