To be a false prophet, Jesus would need to offer the statement as a forecast, a present assertion about a future factual circumstance. Mark's Jesus makes no such offer with respect to the timing of the glory event, and even denies that such a thing is possible in principle, at 13:32.Otherwise, we have 'Mark' as a much later writer, deliberately writing about an unfulfilled prophecy, where no one like a son of man turns up. In other words, 'Mark' would be offering us Jesus as a false prophet.
Forecasts simply are not the only variety of future contingency statements. For example, Jonah wasn't a false prophet, he just failed to realize until afterwards that he was delivering an ultimatum, rather than a forecast.
The thread has already discussed Olivet proper (13:30), wherein language that may well have originally referred to the end of the First Temple is alluded to while the teacher is overlooking the Second. Whether or not the intended reference was to the events of 70 CE, the events of 70 are an arguable fulfilment of what is arguably a scheduling statement, and so whatever the statement actually is, it isn't definitely false.
Some people argue that 14:62 makes the priest an indicator life for the fulfilment of the prophecy. I don't see why the general resurrection wouldn't situate the priest as "foretold."
And finally there's 9:1, which, when crisply separated from the rest of the speech of which it is the conclusion, sounds like a relatively clear scheduling announcement.
However, it concludes a speech which teaches that there are two kinds of death (8:35). One kind is apparently plain language mortality and the other is something else. If you plain-language die in the line of duty, then you don't die the other way.
If anybody standing there subsequently died in the line of duty, then 9:1 in context is in the process of fulfilment. Since Christians believe that lots of people have died in the line of duty, no issue arises among the pious about whether Jesus' statement is false. Lots of people have saved their (second type) lives, and now await the glory event.
Oddly, however, there is now that chapter boundary which invites some readers to view the statement apart from the rest of the speech. The chapter boundary was put there by some Christian. Except for the chapter boundary, there would be no question of Jesus having made a scheduling forecast; the meaning would clearly be what it is and has always been for the "start at the beginning and read through to the end" listener: that some people will avoid an extranatural kind of death by naturally dying according to the approved practice.
When that Christian gratuitously introduced the chapter boundary, the new possible meaning of 9:1 was a false assertion. It follows that some Christians would offer Jesus as a false prophet, because some Christian did make the offer an admissible reading, even though Mark didn't.
That pretty much takes "prophecy fulfilment" off the table as a dating tool, IMO. It shares a foundational flaw with the "criterion of embarrassment" - there is no telling what anybody else finds embarrassing or fails to find embarrassing. Period.