Barker is as accurate as any historian can be and, while the book isn't strictly speaking academic, it was written by one and is well sourced. She makes her arguments according to her interpretation and has a good appendix that addresses the controversy over the numbers of the English and French armies and why she supports the more traditional view over Anne Curry's. Clifford Rogers, in "The Battle of Agincourt", The Hundred Years War (Part II): Different Vistas, makes many of the same observations and uses the example of other well documented French armies from the period (as well as one of the more reliable chronicles) to support the argument for 6000 English and 24 000+ French.

That, I think, is the only major controversy she involves herself in. I'm not sure I agree with her view that the traditional view of the French cutting down their lances to 5 feet while the English used their lances as pikes is wrong, but there's no real evidence either way other than that of "Inherent Military Probability", always an unreliable beast.

Academically, it seems to have been well received. Jonathan Sumption, who has been writing a monumental work on the Hundred Year's War, certainly gave it a rave review (though he tends towards Anne Curry's interpretation of the army sizes), and I've not heard of any negative academic reviews.