Jesus would have returned invisibly in 1936 to take the throne instead of 1914. (According to the method of Watchtower dating. *see below)
If Jesus returned invisibly in 1936 the following could not have happened:
In short, if Jesus returned in 1936, the Jehovah's Witness leadership (the "Faithful and discreet slave class") could not possibly have been appointed in 1919 to lead His organization. This claim to be Jehovah's true spirit-led organization would be false.
On inspecting the remnant of his anointed disciples in the year 1919 C.E., the reigning King Jesus Christ did find the appointed "slave" faithful and discreet in the feeding of his "domestics." Accordingly, he appointed this "slave" class over all his belongings. (God's Kingdom Has Approached, WTBTS 1973 p. 355)
Thus, dating the fall of Jerusalem to 607BC is crucial for the Jehovah's Witnesses. However, every authority outside the Watchtower dates the fall of Jerusalem to 587BC due to substantial evidence found in the Babylonian records.
I've found the best approach to take in bringing this up to a Jehovah's Witness is to wait until he discusses how the Watchtower came up with the 1914 date for Christ's return. When the Witness breezes over 609 while adding up the dates, stop him politely and tell him you've always been taught that Jerusalem fell in 587. Ask the Witness for more information on the matter, especially from any standard/accepted history source. Make him do the digging and wrestling with the issue.
In the meantime, read up on the subject yourself. Online try:
http://www.towerwatch.com/articles/the_1914_doctrine.htm which is an excellent summary of all the proofs for 587. Also see http://www.jwfiles.com/607v587/index.htm which chronicles one man's letters back and forth with the Watchtower Society on the issue.
If you really want to dig deep, get Carl O. Jonsson's book The Gentile Times Reconsidered which is a definitive treatment. You can find the 2004 edition on Amazon for less than $15.
The Witness will probably return in a week with the Watchtower's pat answer on the subject as found in their Insight on the Scriptures. Take the time to read it and craft good leading questions based on your research for his next visit.
*The desolating of Jerusalem and the land of Judah by the Babylonians in 607 B.C.E. marked the overthrow of the Messianic kingdom of David, and hence this is what marked the beginning of the "seven times" of the Gentile domination of the world of mankind. Unalterably, then, the 2,520 years of the Gentile Times began then, and, because of beginning there, they ended in early autumn of the year 1914 C.E (God's Kingdom Has Approached, WTBTS 1973 p. 261)