Recently I got a number of questions regarding the number of days a job is advertised to the public for the different UN agencies. I did a quick and dirty rundown of the numbers based on my 2010 data and they stack up as follows: On average a UN job is advertised for 35 days. The minimum observes was 12.59 days (UNISDR) and the maximum was UN OLA (124.5 days). And between the department / funds / programmes are significant differences. If you want a post with UNISDR (12.59 days), UNDP (14.2 days), IMF (14.89 days), UNOPS (15.23 days) or IFC (16.25 days) you better be quick.
So it is a good idea to start applying as early as you possibly can. Not only you do make sure that the application gets through on time (think system downtime which may strike at any given moment) but also you have chances being looked at early in the process since some long listing processes start while the application is still open. To give you an idea how the overall situation is have a look at the chart outlining the different average advertisement periods.