As far as I know, his research is ok. But his conclusions and analysis were criticized widely immediately after publication.
He was likely correct about the major cause being a volcano, though it seems less likely that it was Krakatoa (his evidence being flakey with his contemporary account not fitting the timeline). Recent evidence suggests that it was a large eruption in Latin America, possibly with a second following a few years later.
Generally, it's accepted that there was a major event in 535-6 which caused global cooling and "dimming" of the Sun. His volcano theory is sound. And much of his research concerning immediate consequences is ok as well.
Where he really gets into trouble is by making very far-fetched claims about the event having direct impact on a number of historical changes. Sometimes those changes didn't occur for decades. Keys dismisses other variables in favor of a direct connection with the 535-6 events. This is absurd. Plus he twists his sources (Krakatoa) to fit with events he wants.
I recall being shocked when I read his theory on how it was responsible for the rise of Islam. He's right that the chaos and upheaval in the aftermath of the event molded the world into which Muhammad entered. But so did a myriad of other factors. Without Christianity you wouldn't have the foundation, without Judaism there wouldn't be Christianity, without the pre-Jewish religion there wouldn't be Jews... and you see the point. Yeah, it's true that Judaism is a crucial factor but it's not THE major cause. There's a ton of variables that lead to the development of the theology and its eventual spread. History is built upon history. You can find a connection to pretty much anything, but just because it's connected doesn't mean it's important. Key's claims that the events were the direct cause of massive global upheaval. They played a role.
Just in case one hasn't read the book, can you explain what the actual thesis is? Thanks!