Update: The developer contacted us to let us know that the update he showed off hasn't been applied yet, but will be released very soon.
At Android Police, we're Android evangelists. It's pretty rare that you'll get us to admit that Apple does something better than Google. But in terms of almost obsessive attention to visual design, Apple has the upper hand. Case in point: the iCal app icon on the iPhone and iPad updates every day, putting the correct day of the month on the icon. Why doesn't Google Calendar on Android do that, years after its inception?
Whatever the reason, you've now got at least one option for that functionality: the previously-covered Today Calendar. Developer Jack Underwood took to Google+ to show off the new feature for Today Calendar, which will now update its app icon every day, just like iOS. This required at least some unconventional programming, or as he puts it, "auto-updating hackyness." As Underwood notes, Google does not have an API for this.
This isn't a widget - the Today Calendar icon will update on your homescreen of choice and in your app drawer, though I think other apps that rely on cached images may not see the benefit. Google, could you please impliment this functionality? It's not as though seeing an updated date on an icon is essential, but it's a nice bit of polish. Well done, Mr. Underwood.