Update 1: The Alternative discussed in comments:
We should show both the Exact and Elapsed at once (for a limited time), as gmail does, and described in T94353#1178467 (this is Quiddity's recommended option), Then, display just the Exact time, with the Elapsed time in a mouseover tooltip.
Update 2: (Copy of description from merged task)
Notification timestamps are all in relative time -- 2s, 2m, 2h, 2d, 2mo, 2y, 3y... While it's useful to see that an event took place "yesterday", knowing that something occurred "3y" ago is the opposite of helpful, since the same timestamp might apply to notifications that arrived 364 days apart.
We can debate what the ideal interval is after which we should switch to absolute time. Mac Mail, for example, goes to dates after "yesterday," while Twitter trips to dates after "24h." We can also discuss the proper form notation should take. One thing worth noting is that as long as dates are within the current year, we can safely drop the year from notation. Whether "within the current year" means within the current calendar year or the current trailing 12-month can, again, be debated when the time comes.
Many users like the new "Elapsed" timestamp e.g. 4 hours ago
Many users prefer the old "Exact" timestamps. e.g. 16:11, 4 October 2013 (UTC)
This is especially relevant for anything more than "1 day ago". Anyone trying to closely follow the order of previous posts, has to mouse-over the flow-timestamp in every single post, to see when it occurred.
(Original/alternative idea: This could be added as a user-preference. Possibly, it could be as a checkbox labelled "Use elapsed-timestamps in discussion pages by default" (or similar), under "Date-format" at Special:Preferences#mw-prefsection-rendering.)