I have the same issue that started within the past two days. Have you found any answers to the issue?
In the meantime, I've disabled Alerts in the modules that are running and everything is fine. If I turn them back on, the site messes up. However, I am getting a CRON error every time the script runs.

I agree that I am also having the same fatal error which totally crashes my entire site.

TupeloWx is correct... Whenever the Alert function is activated within the ZWeather module, anyone trying to access the main web site gets the error message, "Fatal error: Call to a member function getTagName() on a non-object in /(...site name withheld)/components/com_zweather/zweather.class.php on line 831."

It should be noted that I do have a ZWeather module included to the local weather on the site's home page.

Thanks to TupeloWx's suggestion, I found that if I deactivate the Alert function in the ZWeather module, everything goes back to running normally. The site worked fine for the past several weeks using the ZWeather component and module, but suddenly started crashing the site late last week. And, as GJShaller stated earlier, nothing on the server which would have anything to do with the ZWeather package had been changed within the last week.

Is it possible that the National Weather Service has changed their alert transmission coding so that this software package needs to be adjusted in order to pick it up?

If nothing else, there should be some sort of a fail safe "escape" routine written into the code so that if a NWS feed is corrupt or can't be found, that the program simply displays a message like "Alerts Currently Unavailable" or something similar instead of breaking the entire site. Is that possible?

For what it's worth, in the ZWeather component Global Configuration, I have the HTML cache and the icon cache turned on, and the Cache Refresh Mode is set to "Foreground Cache Refresh."

Hats off to the developers for a wonderful piece of software. I really do love the ZWeather package, but my clients won't tolerate their entire site being taken down because of a bug in the Alert code. For the time being, in order to keep the site up and running, I am letting the ZWeather package run without the capability of displaying any alerts. To me, the alerts are an important feature - if nothing else - from a public safety standpoint and I miss not being able to display them. Hopefully, a fix for this can be released soon.

For whatever reason, things began working again yesterday. I checked to see and my CRON tasks were completing again so I re-enabled alerts and it works fine. I would seem there was something going on with the NWS server(s).
And yes, a routine in the code to say that alerts aren't available currently would be nice but it seems this wonderful piece of software is on the far back burner. If I had the technical ability I would offer assistance to Dan, the developer, in getting bugs worked out.
During the time of this problem, the sites that I'm running with the older version of ZWeather continued to work properly. There are a few other things that the original version does better also.
Anyway, turn your alerts back on and see if it's working now.

Thanks for the heads up, TupeloWx. I checked and the ZWeather module does appear to be working again so it seems likely that there was something amiss in the NWS feed for a few days.

Regardless, since we are dealing with an unknown situation and there is no guarantee that it won't show up again, I think I will leave the alert function of the module turned off (hidden) until this bug is worked out. It's not worth risking my client's site going down again until a fix or workaround is released for the problem.

It is a shame, too, because this really is one of the cooler modules available for Joomla! Here's to a quick fix so we can enable the full feature set again soon!

I'm glad it's working for you again. I have no idea how long you have been using the script but this the first time for such an error for me and I've been using it for 3+ years.
Either way, I understand not wanting the problems. Maybe one day this will reach maturity. I've previously offered and would gladly pay for Z Weather if the bugs were fixed - as I'm sure many of us would.