And the clock icon never shows the correct time. It seems like the calendar app is a hack to get it to work right.
I now run Android and have Beautiful Widgets showing me the correct weather. :)
The weather widget in iOS 5 is a better compromise, it just quickly grabs the weather info when you start pulling down the notification drawer.
A friend was going nuts going OMG OMG THE WEATHER APP UPDATES LIVE NOW. It turns out it just happened to be 73 or whatever degrees out at the time after he updated.
For these small things like weather updates I agree that apple needs to allow developers to update the app icon or whatever with some alert system on the home screen. It wouldn't be overly difficult to implement.