I just checked on KBS's site, and the final episode, 24, ran one hour and twelve minutes thirty seconds. The VOD file they have there (which I did not watch beyond the first few seconds) does not have any opening titles, so it may run for a minute longer, but not two hours.
Maybe someplace they showed the last two eps back-to-back?
One hour, twelve minutes just about jives with TAN's broadcast of that final episode. I don't know for sure exactly how long it ran (my stupid tape ran out towards the end, so I can't verify ) but I do recall that the final episode started a bit earlier than usual that evening, and therefore it did run a little over one hour in length.