I had no idea some of the public 'mechanical' clocks you see around Belfast are radio controlled from Rugby, and that the reason they show the wrong time is because, although the clock knows the right time, there is no drive mechanism to the hands to correct the time as it changes by an hour twice a year (if I understand this article correctly).
http://news.bbc.co.uk/1/hi/northern_ireland/3629031.stm
MSF signal page.
I remember someone telling me that a clock that has stopped is much more accurate than one which is not, because it reads exactly the right time twice a day. Whereas most of our clocks and watches are not accurate at all....what a load of cobblers!!