Just for the record I've had one of those "times", it was about 04.00 hrs (UK), on both iPad and iPhone the Weather Widget just kept refusing to update again - and not just the temps but also the hours (think the "Now" was stuck on 22.00 hrs. This went on for a good 10 minutes while I kept messing around switching between devices and opening Weather and News Apps until finally the Widget updated, funnily enough again on both devices.
The reason I play around with the Weather and News Apps is that they both have links to weather data, the Weather App obviously but the News displays current temp in the top right corner. Although I've never seen the Weather App fail to update the News App does sometimes have the temp data missing (although my location is still shown) and the only way it returns is to close and reopen said App.
Not sure if there is a "working connection" between the above Apps and Weather Widget but have noticed when those Apps are opened and I see the Location Services arrow briefly appear in the top of the display I will then usually see the same arrow appear if I quickly switch back to the Widget, and if Location Services is triggered by the Widget it almost certainly updates thereafter.
With respect to "time", prior to 04.00 hrs the Widget of both devices was updating ok for the previous 20 hrs or so, and as I type this still ok, so what gives - I'm thinking is it really server related and at certain times a connection just fails or is it something to do with location services within the devices themselves just not being triggered correctly, either way this is a strange bug.