Your question is a bit disjointed and rambling and I don't exactly know where you are coming from, so let's start by clearing the air and getting us all on a level playing field.

'Preterism', for those playing at home, is an interpretive approach to Biblical prophecy and its teachings about 'the last things' (eschatology). Preterism is the view that what is described in prophecies, and we're especially talking about the Revelation to John, either primarily or completely refers to events that occured in the 1st century, so that those events are past. (praeter being a Latin preposition that includes the idea of being past or beyond something, and particularly so when used for as 'praeteritum' to mean past in a temporal sense).

It's three main alternatives within the history of Biblical interpretation are Historicism (that the book of Revelation may be mapped out as occuring in history up to and beyond the present day), Futurism (that the book of Revelation concerns primarily future events, and little to none has yet been fulfilled), and Idealism (that the book of Revelation portrays an idealised, not an actual, conception of reality that is not meant to be identified with specific events past, ongoing, or future).

Specifically on 666 and 616, it's not really 'conspiracy theory crazy' to identify these with Nero Caesar or another figure, because writers of apocalyptic works wrote in a world where various types of numerology were current and expected in their works and would be understood by their audiences. Essentially it's a code between reader and writer.

Okay, I realise I haven't quite answered your two direct questions: how common and flaws, but what does the first question mean - how common among historians, or among biblical interpreters? What exactly do you mean by 'main flaws? Where to from here OP? Do you want a better articulation of the contemporary Preterist school of thought? A history of Preterist interpreters on Revelation? A quick number count on scholars?