I find the date of the destruction of Jerusalem a really strong argument, because without it there's nothing to show that we're in the last days.
Also, the two classes of Christians doctrine, which has incredibly weak Bliblical justification. The "other sheep" are the Gentiles - an interpretation which never occured to while I was a JW. There's no good reason to say that the "great crowd" and the "other sheep" are the same thing. It makes it harder to interpret the parable of the sheep and the goats - how does this work if there are two different types of sheep?
I think historical arguments are harder, because it will be claimed that ancient chronologies were altered for political reasons. You'd have to have a lot of knowledge to argue along those lines.
There are other killer arguments. One idea that is common among JW's (but seems not to have been officially taught for a long time) is that humans didn't eat meat until after the flood. Yet arrowheads have been found in the skeletons of mammoths, which are supposed to have been made extinct in the flood (see the picture in the Bible Stories book). There are convincing arguments why the date of Passover is not Nisan 14. The flip-flops (superior authorities, generation). Picking and choosing what parts of the Bible to view as symbolic (hellfire, destruction of the earth).