Earlier quoted context omitted.
The show itself used quite a few very interesting methods to do it. Basically, L played a lot of hunches and won big several times. The part about the time of day was found out long after L had narrowed things down to a small region of Japan by provoking Light into killing someone who appeared on a "worldwide" broadcast that was actually only broadcast in Light's prefecture. The time of day part was actually used to…
One problem with the article I realised earlier was that it described the broadcast to Kanto as a gamble because it wasn't broadcast anywhere else, which is wrong. It was broadcast in each region one after another to find out which region it was in. It wasn't a gamble at all, it was a very clever way of finding out where Kira was watching from.
But it never really turned out to matter, as you say. L was able to notice that weird case where the evil guy who had taken school children hostage died of a mysteriously timed heart attack and piece a lot of things together.
Actually, though, that broadcast was probably one of the most important puzzle pieces. He was able to prove that Light could kill remotely with nothing but a face & name, having cut a special deal with a criminal and kept the guy under special observation the whole time. Light was very careless there.