My two cents:

1) It should attempt to detect location and display that to the user.

2) You can save locations but, these are lost on refresh.

3) No way to specify Celsius.

4) It's not a very simple service. I should be able to bookmark this and click on the link to view the weather. Instead, I need to type a location every time. Right now, I just have a bookmark to "https://www.google.com/search?q=weather".