For what it's worth, there *have* been issues with 4.3. Many of these should almost be expected whenever a new version of software comes out, including things like certain apps not working or frequently crashing, but there have also been issues with getting root working correctly with SuperSU, as well as other "under the hood" stuff. Again, it's almost naive to think any software will released without a few bugs, and I wouldn't be surprised if 4.3.1 comes out sooner rather than later to address some of immediate concerns...but I certainly don't think that Google "released the wrong software".
Having said that though, 4.3 is for the most part pretty solid, and to the average end-user should be running just fine. I also have it on my Nexus 10 and haven't had any problems whatsoever.
To the OP: At the moment, only Nexus devices (as far as I know) have 4.3 at this time. The Google Editions of the HTC One and Galaxy S4 should get 4.3 updates fairly soon, which means that one could get ported over for the Verizon version, but it take some time, and it will be even more time before any "official" versions get released for this phone I'd believe. To your second question, if you don't have service with Verizon currently on your phone, I highly doubt you'll be able to update OTA. You will most likely have to flash a factory image or ROM once available if you want the update. And yes, if you want to keep up-to-date on this subject, the
forums over at XDA are a good source for this sort of thing.