I've spent the day trying to find an answer to this widget problem. I believe I found the solution on another android board.
A woman named Karen said this:
I did have them problem with the homepage digital clock/weather widget. I went to the store and sales man showed me how to fix it. Works great again. Went to my friends the same night and hers was also not working. I did fix her phone the same way and she is happy again too.
Go to your settings from your home screen. Hit applications. Hit manage applications and wait for all to load. Find the little sun that refers to weather BY HTC and the little cards that look like settings cards BY HTC. (because you might have other weather programs you don't want to erase them) Make sure you find every icon for weather for HTC and erase the Data and the Cache. If you don't get them all it wont work. Once you have done this you can try and go to your market and drag to remove your weather icon if you like but it did not work for me. It is a factory setting I guess. Next go back to your home screen and hard press the screen at the top. When this happens select HTC Widget and then CLOCK. Scroll to the clock weather widget and tap it. Select current location or type one in and hit done. I promise it worked for me and it should work if you erase ALL AND ONLY HTC ICONS THAT REFER TO YOUR HTC WEAHTER. Good Luck! If all else fails do like me and take it to the store THAT HAS SERVICE TECHS. CALL BEFORE YOU GO.
****I did what she suggested and IT WORKS as long as I don't put my town in. Now the widget is the correct time but I don't see my town and no weather! OY!****