I have to write the administrator of the server requesting the permissions to be changed. It seems the component folder is at 'read' for group level. Once they take care of that, I'll update on my status.

Thanks for the feedback. I will look into it and update the code for the next release.

Version 6.0.2 has just been released that addresses this issue. The fix was a little bit more involved than jimp's hack. The issue actually was the NWS dropped the time zone designation in the current conditions time, and instead is now using just the time offset. Z Weather was using the time zone designation to determine the local time (i.e. EDT, CST, PST). the program now uses the time offset (i.e. -0500 for East Coast locations). If you don't want to do a complete re-install, you can just replace the zweather.class.php file to the components/com_zweather folder with the one in the 6.0.2 release.