I'd have to dig up in several books.

I remember one critic concerned his discussion of economy. It's not very early - medieval at the earliest, perhaps renaissance. I'm really not that well-versed in pre-1000 matters, it's not been yet a huge focus of mine.

I remember the book too. It's from a rather scholarly and arid (yet somewhat fascinating) tome on the Venetian silk industry of the renaissance. In the part of the book surveying economy more generally, the Historian deplored the fact the general public still had almost only Norwich to fall back on, when his discussion of economical matters was so outdated, relying on views dismissed now for decades among historians of economy.

I also remember another book. This one is a textbook collecting documents in latin and old Venetian, translated in English. It's meant for beginners in Venetian Studies, who haven't yet mastered the language. It's that author who recommends Norwich as the best narrative history available in English but warns the students most of his interpretative framework should be regarded as outdated - that the book would need serious revisions in this regard. He points readers who read Italian to Alvise Zorzi instead. For having read a few of his books, Norwich is more fun, has a lot more details and is just a better read. As far as I can tell, Zorzi does a much better job with context and perspectives, though.

It's also in that book that the editor offers a text by a famous Venetian diarist/chronicler, and goes on explaining documentary historians had recently established his works were unreliable - down to parts that are complete fabulations/fabrications. All sort of things are wrong... dates, attendants proven not to have been there, descriptions of events not matching inventories/purchases, anachronisms etc. Then he comments that several reputed Historians would need to update their books, including Norwich who used those documents as his only source for a few things, including a whole chapter. It's been years, so I'm not sure anymore what it was, but it's nothing catastrophic, like descriptions of celebrations, or funerals. Elsewhere he was also criticized for having used as factual sources without warning the reader documents that are known essentially propaganda commissioned by the Doge and highly unreliable.

Then again in a book on social classes during the renaissance, the author in the intro comments on the fact the general public's only easily and widely available introduction to the topic remains Norwich's History of Venice, and Norwich's descriptions and views are incomplete and outdated.

Somewhere in one of those, the writer mentions it's been decades since Norwhich's book, that it remains the reference for the general public but that a modern work of the same scope reflecting all the big advances in the field since History of Venice is badly needed in English, existing for now only in Italian.

It's a bit the same in French. Norwich translated, Fernand Braudel (who is in another class altogether), some Zorzi translated. You really need to pick one of Braudel's books eventually. Capitalism and Material Life, 1400-1800 should be up your alley, so would be The Mediterranean. And perhaps Aspetti e cause della decadenza economica veneziana nel secolo XVII. Read it in French if possible, though some of his works were written in Italian, and I think one or two are only available in English. You might want to check wikipedia first - the article in English is better. I don't know enough your views on Economy to judge if Braudel will be great, tolerable or plain annoying to you. It's full of things I've rarely seen elsewhere, and his approach is unique