Sounds like I've got a BSP hole (thanks for that link, Crusha). I suppose I used an incorrect method the first time I created the tower in the center of my map.
The first time I made a 12 sided, hollow cylinder and then used geometry mode to add a opening to each side. This method caused the invisible block.
The second time I made the cylinder normally and then subtracted BSP blocks to make doors. No invisible blocks this time.
It just seems strange that either I didn't notice the BSP hole at first or that it appeared later.
Thanks for your help.

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