I know of the time notation for some anime—between 22:00-27:00. I know that this indicates that the show airs at a particular time, and likely targets a particular audience.
Why would this notation be used, and be preferred over a more traditional 24-hour format?
This is a hypothesis: The time goes beyond 24 hours in order to make it easier for the viewers to identify which day of the week they should stay up late to watch the show. For example, "Hayate no Gotoku! Cuties is aired on Monday 25:35" informs the viewers that they need to stay up late on Monday.
If we write in standard 24 hours format Tuesday 01:35, it may cause some confusions:
In Japan, both 24-hour format and 12-hour format are used in everyday life activity. Therefore, a time without any indication of the period of the day such as Tuesday 01:35 might be confusing. The confusion may also be partly attributed to the cultural perception about the hours of darkness.
Quoting the Wikipedia article1 (emphasis mine):
1 The Wikipedia article lacks citation, though.
Times past midnight can also be counted past the 24 hour mark, usually when the associated activity spans across midnight. For example, bars or clubs may advertise as being open until "26時" (2am). This is partly to avoid any ambiguity (2am versus 2pm), partly because 8the closing time is considered part of the previous business day, and perhaps also due to cultural perceptions that the hours of darkness are counted as part of the previous day, rather than dividing the night between one day and the next.
There is another notation that is commonly used, where the day of the week is the day that the viewer has to stay up late, and the time is clamped to 24 hours with some text to clarify the time. Using the same example as above, in this notation, it will be Monday, late night at 1:35.
For the purpose of reference, I do a sampling from the anime of Spring 2013 season (late night shows only):
Beyond 24 hours:
Clamped to 24 hours, but the day of week is the one before:
The usage of the 2 notations are more or less equally common. We can also observe that it is more common to specify only the starting time, than specifying both starting and ending time. The data might be skewed by the fact that all the shows here are late night shows, and the sample size is quite small (17 shows).
From Wikipedia:
Time-of-day notations beyond 24:00 (such as 24:01 or 25:59 instead of 00:01 or 01:59) are not commonly used and not covered by the relevant standards. However, they have been used occasionally in some special contexts in the UK, Japan, Hong Kong and China where business hours extend beyond midnight, such as broadcast-television production and scheduling. They also appear in some public-transport applications, such as Google's General Transit Feed Specification file format or some ticketing systems (e.g., in Copenhagen). This usage prevents a time period reported without dates from appearing to end before its beginning, e.g., 21:00–01:00.
Whist in Japan, I've seen this happen in other places outside of anime. The opening times for one onsen was 18:00 - 20:00 for women, 21:00 - 25:00 for men.
I'm pretty sure it's to avoid the break that happens when switching days. It's easy to see that the men's bath is open for 4 hours, but 21:00 - 01:00 isn't so obvious at first glance.
It's also related to waking hours - if you're up at 1:00 it's more likely that you've stayed awake rather than woken up early. In that vein, keeping the same day's hours could potentially be less confusing
For most tv this is a time zone issue to include all areas covered within one "day"period
