Humans represent time vaguely rather than precisely. Computers tend not to.
A while back, the British Library catalogue was put online as linked data. The library cataloguers had added details of author birth and death years but not always birth dates. But the data model normalised "1941" to "1941-01-01". (They fixed it after I moaned on Twitter.)
You should be able to represent in your data model, date-time library etc. vague dates and relative dates. When I say someone was born in 1941, I don't mean they are born at 1941-01-01T00:00:00Z. When I say that something happened on Thursday, I don't mean it happened at 2013-01-17T17:04:00Z. It may have happened at any time on Thursday.
If you store everything as Unix epoch seconds, good luck representing vagueness.
ISO 8601 gets around the problem rather neatly by being big-endian and allowing omission at any point. Wanna say 1941? "1941". Want to say January 1941? "1941-01". Want to say January 14, 1941? "1941-01-14". Want to get very detailed? You can add points of a second: "1941-01-14T12:14:03.0482Z". You can do timezones.
Eventually, we'll have an even better way of representing date-times that are more like bitmasks. We can then represent in a sane way the concept of opening hours. If you say the shop is open from 9am to 4:30pm Monday to Saturday, how do you do that?
If I am digitising an old text of unknown origin, and on a page it says "January 12", and on the page after that it says "January 15", can I represent those with a reference to an implicit but unknown year? I don't know the year, but I do know that the January 12 instance comes before the January 15 instance on the next page. And at some future point, we might deduce from circumstantial evidence what year it was and the sequential ordering will still make sense. Relative dates would be useful here.
ISO 8601 allows you to represent ordinal dates (the number of days since the beginning of the calendar year).
Can your date-time representation deal with moveable feasts like Easter?
Have a look at the WHAT WG Wiki page on Time to see more obscure use cases: http://wiki.whatwg.org/wiki/Time
Your date-time representation, storage format and calculation libraries are probably inadequate.