Which are the most mysterious tall structures?
I would say to these belong the masts of Qurayyat Transmitter (
http://skyscraperpage.com/cities/?buildingID=104692,
http://skyscraperpage.com/cities/?buildingID=104693 ), which are too remote situated for broadcasting sites and which are surely used for transmissions on UHF/VHF-frequencies as one can clearly see on satellite picture a thick cable running up. I believe they are used for a radar warning system, but I have no evidence of this theory. There are also no pictures of these masts available.
Also very mysterious is Umm Qasr TV Mast (
http://skyscraperpage.com/cities/?buildingID=107176 ). I believe, it was used for transmitting propaganda TV to Iran in the 1980ies, but have no proof for this theory. Also interesting: when was it built by which company.