Suggestion (not necessarily a valid Answer since I do not own a copy of this edition and cannot verify to what extent it is annotated with modern information) have you investigated this edition from Hugh Trevor-Roper (pub 1993, this edition is a 2010 reprint)? Some of the customer reviews indicate it has factual corrections, such as this:
The merit of Gibbon's masterpiece needs no defense. Readers are, I assume, looking for remarks about whether this Everyman set is a quality edition. Well, this is it. I looked at the Folio Society edition: lovely, yes; but fragile and grossly overpriced. The Everyman is sturdily bound with solid boards and paper. The typeface is clean. A handy bookmark is bound into each volume. It's nice to hold in the hand.
The text is the standard one of 1910, with notes to catch major errors of fact; there are good, more recent introductions (to vols 1 and 4) by the eminent Hugh Trevor-Roper (does that man know everything, or what?). ALL of the original footnotes are here, and readers of Gibbon should consider them as essential. Someone once quipped that Gibbon lived out his sex life in footnotes; there's some truth in that remark. [emphasis added]
Edit by OP: This is indeed an excellent edition for this purpose. Here's an example, from page 4:
Note however that the corrections are from no later than 1936; for more up-to-date information, the book refers readers to the enormous and exorbitant Cambridge Ancient and Medieval Histories ("which contain detailed bibliographies").