I think it's main disadvantage comes straight from its power. One of the most common things done in OOP is to replace parent classes with derived classes in some places, to specialise the behaviour of the code. Well, if not done carefully, it's easy to invalidate some of the assumptions made in the caller code; and that could be very difficult to spot while reviewing the code, because the types you're seeing declared are not the ones actually being used.
In brief: polymorphism can be made not explicit and thus easy to overlook weird behaviours in the derived classes.
