I could nitpick it on a hundred tiny points, but (speaking as someone who specializes on post-Roman Britain), I think the first book (which is the only one I've read so far) is one of the best portrayals of the period in fiction that I've ever read.

There's ongoing debate about the extent of urban decay in Britain. It's clear that, around the end of the 4th century, a lot of villas are being abandoned (probably even before the legions left in 410). It's less clear precisely when cities were abandoned: new building ceases by the end of the fourth centuries and the cities were then filled with layers of 'dark earth' (a pseudo-technical term for silt). This dark earth might indicate abandonment, or it might be all that's left from the buildings being inhabited by people who didn't care about sweeping up their organic waste (human and/or animal shit); debate is ongoing. But it seems like, during the fifth century, people gradually moved away from old Roman structures to new farms, villages, and hillforts. The old Roman buildings where then slowly recycled for raw materials (lead, iron, stone, etc) over the following centuries.

Were the fifth-century British unable to maintain the Roman buildings, or did they simply not care for all the upkeep required by stone walls and tile roofs? Did people prefer the more organic, impermanent architecture of wooden buildings (like we do in modern America)? Or did the economy collapse so severely that it was no longer possible to maintain the infrastructure necessary for repairing Roman buildings? The latter view (economic collapse) is most popular among historians and archaeologists, though there's some disagreement (for an overview: G Halsall, Worlds of Arthur [2013], R Fleming, Britain after Rome [2011], A Rogers, Late Roman Towns in Britain [2010] - note the recent dates of these books, this is very much an ongoing conversation among scholars).

The one thing that could be improved the most in the first book is Cornwell's description of the Saxon invasion. The book was written a long time ago, and historians have reconsidered many aspects of the narrative he's relying on. It's pretty clear now that there wasn't a sweeping wave of invading Saxon barbarians - most Germanic immigrants appear to have been farmers, and their migration into England was unorganized, small-scale, and relatively peaceful. They also didn't cover themselves with fur, wear horned helmets, or use giant axes. But I can forgive Cornwell that much, because the world he creates in Western Britain - of Roman ruins, cultural change, religious competition and confusion, and small communities led by petty warlords who can only muster a few hundred spears in their largest battles - evokes the fifth century beautifully.

I would recommend Fleming's book (cited above) for the best overview of the period. Halsall (also above) sums up the interpretive difficulties of the textual and archaeological sources very effectively, and gives the best historian's answer to the question of the historical Arthur out there.

I need to get my hands on the rest of Cornwell's series. I found the first in a used book shop while excavating a 6-7th century Anglo-Saxon mead hall this summer, and it made me very excited to resume digging every morning!