When filtering, relative dates and ranges are great. "Today", "yesterday", "last 7 days", "this month", etc., are much more user-friendly than manually entered date ranges.
Unfortunately, I've noticed that an increasing number of sites are now using dates like "4 days ago", "Tuesday", or "Nov 3rd" instead of absolute dates in pages and listings to specify key information such as publication or upload dates. There are a number of problems with using relative dates in this manner and I address the three biggies below.
1. Relative Dates Force Readers to Perform Calculations
I know there are some who will dispute this point, arguing that relative dates are easier to understand when used properly. And I will not deny that "yesterday" or "a week ago", for instance, seem easier to grok than "June 13, 2009" or "June 7, 2009", but these are edge cases and their utility degrades rapidly with the passage of time.
When I see something like "uploaded Nov 3rd", my instinctive reaction is "WTF does that mean?". Then I have to slow down and think "well, if there is no year included, it probably means that it was uploaded within the last 12 months, so let's see... this is June, 2009, so that means that it was probably uploaded Nov 3, 2008". Would your grandmother, who has trouble turning on her computer, be be able to figure out what was meant?
Even a reader familiar with the convention will be distracted and have to waste valuable processor cycles translating the relative date to an actual date. It is even worse when dealing with seach engine cache documents. What does "3 days ago" mean when reading a Google Cache document? Sure, you can scroll to the top, note the date that the document was cached, then relocate the part you were reading and compute the actual date, but now you've had to actually stop and go hunting for the additional information needed to perform the calculation.
2. Relative Dates Cannot Be Trusted
I said "probably" in the section above when describing the process of figuring out the actual publication date because the ommission of the year could have been accidental. Even when it is clear that the use of a relative date is intentional, such as "3 days ago", there is no way to be sure that the document being viewed is current.
There are many layers of caching between the typical web page and the typical web page reader. Many web servers/farms have a caching layer, many ISPs employ caches in an attempt to save bandwidth, many companies have caching proxy servers. Many of these caches are misconfigured (or intentionally configured) to ignore Expires headers. Many web pages do not bother to include Expires headers. You get my point.
Worst of all, many non-web-developer-types do not know much (if any) of this and will never guess that the document that says it was published "Today" is a week old and came from a cache.
3. Relative Dates Are Bad for SEO
Search engines like to know when something was published and often give more weight to fresh content. As near as I can tell, they pretty much ignore relative dates.
Don't believe me? Do a Google search on just about anything. You'll see some results that lead with the date in the little blurb beneath the link and some that have no date. What you won't see is "Tuesday" or "3 days ago".
Search engines will not attempt to translate a relative date to an actual date. There is a simple reason for this: it may know when it first crawled a document, but it has no sure way of knowing when that document was actually published.
The relative display of the date will eventually age out and be replaced by an absolute date but many of the algorithms floating around out there take a year before they switch over. If you're lucky, the search engines that matter will re-crawl your page and will then know its publication date. Sadly, by then your content will be a year old and already stale. Boo-hoo for you.
A Better Way
Misguided ideas about usability aside, I suspect that many sites adopt relative dates because they are less impersonal than absolute dates. "Yesterday" feels warmer and fuzzier than "June, 13 2009". And I get that this is important for sites looking to make a connection with their users (and what sensible site isn't?)
If you believe your readers or site will benefit from relative dates, use both. For instance, you could display dates with an absolute part and a relative part that changes as time passes and is dropped entirely when no longer useful.
For your publication date, use "Yesterday, June 13, 2009" or "10 days ago, June 4, 2009". It's easy for both users (whatever their preferred mode of reference) and search engines to understand and will cause no confusion even if cached.
In lists and grids, I think it is best to stick to absolute dates, but it would not be a bad thing if items were grouped into bands, Outlook-style, when sorted by date.