My post here covers the major errors and I also recommended a few short books on the Eastern Roman Empire that are more accurate. It at least tried to present a more accurate version of history (compared to the popular view of the 'fall' of Rome), but it is a bit simplified and tried to impose modern attitudes on the past, such as by suggesting that Phocas was a bad emperor because he persecuted people - he was a bad emperor by many standards, but you can't really explain his lack of popularity by his religious attitudes. I don't think I've even read about him persecuting sects (though that might be because we have very few sources for his reign), and his predecessor Maurice is a much better example of a persecuting emperor anyway!

Feel free to ask me any questions you have about this period :)

One sort of funny one that jumps out to me is that it says Heraclius funded his military expedition with "donations from the church." That's a really polite way of describing what he actually did which from my understanding was to basically confiscate church altarpieces, candlesticks-- anything made of gold-- and have it melted down to pay off mercenaries.