The typical Preterist position usually involves a fulfillment of most End Times scriptures with the fall of Jerusalem. To this end, it is also usually required that the great harlot Babylon of Revelation 17-19 be interpreted as Jerusalem, and not Rome (see here for a further discussion of that interpretation).
In the zeal to see all things accomplished, many details of the text, most especially those after Revelation 11, are minimized.
One group simply points out the difficulties stemming from Revelation 13 (see here for that statement and a more detailed response). They list the beast, the false prophet, the mark of the beast, the image set up of the beast, and the many other intricate details of the chapter as sufficient proof that these things were not fulfilled in 70 AD.
In short, the events of 70 AD do not fulfill the requirement of the book of Revelation, however, the events of 60 AD – 476 AD, do fulfill Revelation 6-19. The Millennium would have been the middle ages (see here for more on that), which would mean the the dragon has been both incarcerated and released already, and is now at work, and has been for the relatively short period of around 500 years of deceiving the nations and gathering them together for war against the Saints and Jerusalem (Ezekiel 38-39, Revelation 20). Interestingly enough, this seems to be what we see escalating in current events, and the Gog Magog war has been a high topic in the discussion of current End Times events for nigh on 20-30 years at this point.
Clearly, a 70 AD fulfillment is a weak position at best, as it minimizes much of Revelation. Only by saying that the prophecy “starts over” and re-tells the destruction do most come with any even seemingly sensible attempt at an explanation. This becomes unnecessary, however, as you see the events of the second half of Revelation fit very well into the time leading up to 70 AD and the centuries following. Since a “says what it means” approach is apparent from a look at this timeline of history, and it is a simpler understanding, it is therefore, in general, superior to an explanation that must go to great lengths to explain itself.