The most potent argument against 1914 is not necessarily the overlapping generations issue or the 607 versus 587 but the assumptions that this account in the Bible can be used to calculate anything of any worth.
First off, neither Jewish nor Babylonian years were 360 days long. They were based on very complex lunar cycles. The solar years, on the other hand, were 365.25 days long. This (let's subtract the fraction .25) gives out a result of 7 X 365 = 2555 'days'. So add 35 to 1914 and get 1959.
I would not even get into the 607 vs. 587 issue as the individual might think that the Society has better information than all scholars.
Then secondly I would point out that the 'typical' king - Nebuchadnezzar - was supposed to have been insane for those 7 years but was given his sanity back after they were complete.
How does this figure out for the 'anti-type', all the nations of the world, which were supposed to have been insane like that king during those "Gentile Times" but got even more insane in 1914 with all the commotion that World War I started?
It made better sense with the original 1914 teaching which had 'Armageddon' starting before 1914 with the Millennium starting in 1914. But they had to change that when world events falsified their 'prophecy' and they adopted the newer explanation (which they changed again in the 1990s.).
They were not able to reconcile everything in their new 1914 teaching.
Those are their two major weaknesses.