Q&A

It's seldom noticed that the Greek text of Matthew 24:34 uses a grammatical form called the ingressive aorist. Taken literally, this means Jesus DID NOT SAY the generation He was speaking to would live to see all that He said come true. But that they (or the Jewish nation) would not pass away until everything He said started to come true. When understood this way, His words were fulfilled to the letter, because the first thing He spoke of was the destruction of Jerusalem and the Jewish temple. Whether He was speaking of the generation then living, or of the Jewish people, His words were true, because that destruction began in that generation. In fact, in the parallel passage in Luke 21, He speaks of the Jewish people being again taken into captivity, and being scattered among the nations, while Jerusalem is being "trodden down by the Gentiles until the times of the Gentiles are fulfilled." And this would seem to imply a long time. Furthermore, the following quote suggests this is how the church understood Christ's words in the earliest centuries of the Christian era.
"...prophesying concerning the temple, He said: 'See ye these buildings? Verily I say to you, There shall not be left here one stone upon another which shall not be taken away; and this generation shall not pass until the destruction begin."
(Clementine Homilies, Homily III, Chapter XV.)

Note: The Wailing Wall (which was part of the Jewish Temple in Christ's day, remains to this day, and may be part of a future 3rd Temple) stands as a witness that the judgement Christ spoke of was only begun (not finished) in the first century.