Higher oil consumption of synthetic oil in older vehicles.This is a common warning often offered without much explanation. "Synthetic finds leaks" is a way it is often worded. The actual process or theory, as I understand it is this. An old engine that has been running conventional oil for all its life will typically be a bit clogged up with deposits from this oil. Where they have built up over seals, those seals will no longer be kept pliable and good by constant contact with fresh oil. As such, they may dry out a bit and no longer serve their function. However, the built up layer of crud will prevent the oil from leaking.Synthetic oil, since it tends to run cleaner and effectively remove the old deposits from your engine, will excavate those seals - and reveal the leaks.
While this exposes some truth to the theory, what it really means is that your engine could use a few new seals - and that the cleaning process afforded by the first fill or two with synthetic is highly beneficial, since there will be similar sclerotic build ups in places where the oil should run freely, like the passages through which it flows.