The ESPN widget is installed with the OS - it is Apples responsibility to keep it functioning as far as I can see.
Widgets are just a bunch of javascript & html, look at this file…
"/Library/Widgets/ESPN.wdgt/parser.js"
Part of that file lists what appears to be the URL's for retrieving the online data…
gLeagueArray ['RPM'] = {
staticEnable: false,
title: "Auto Racing",
kind: 'racing',
feed: 'http://wu.apple.com/rpm/bottomline/xml/race',
url: 'http://sports.espn.go.com/rpm/index',
background: 'racing.png',
scoreParser: scoreParser_racing
};
The feed URL is broken - the widget cannot get the info because the website changed. You can either work out where the feed should be & correct it (make a copy of the widget first) or report it as a bug to Apple & hope they fix it.
http://feedback.apple.com/
I don't know about the Movie theatres widget - it never accepts my location, so I just get US movies that may be accurate, I don't care enough to test & can't see the feed URL in "/Library/Widgets/Movies.wdgt/parser.js"
Frankly I think you would be better off finding the relevant page with the info you wish to follow & then using the 'open in dashboard' feature of Safari to make your own widget. Be sure to customise the Safari Toolbar to add the 'Web Clip' (open in dashboard) button.
It's not clear if web clips are still a feature - I'm not on 10.11.