I understand that it's difficult, but it should be possible by using individual overlay images for each timezone, rather than just highlighting the whole sector. I suppose one might have to tweak the map projection too. As it is right now, it isn't really that usefull as a tool (it's a neat looking toy in any case though).

Edit: Also, it has "business hours 9-5" on it. 9-5 isn't correct in all countries (Finland 8-4).