Sartre has a famous counterexample in "Existentialism is a Humanism." He asks us to ponder the following case. Think of a young student in France during the French resistance in WWII. The student lives with and takes care of his ailing mother; both the student's brother and his father have died in the war. The student is faced with staying home to take care of his widowing mother or joining his comrades in the resistance. If he stays home, he treats his fellow comrades as mere means. If he goes and fights, he treats his mother as a mere means. But the choice is jointly exhaustive and mutually exclusive---he has to do one or the other and doing one means not doing the other.
The same structure of counter-example can be generalized: there are pairs of jointly exhaustive and mutually exclusive choices such that the value of the choice cannot be decided in advance by the categorical imperative. To find other counterexamples you can just think of situations with this structure. For example, you have an obligation to respond to your mother's phone calls. Yet in buying the iPhone you treat the factory workers as mere means---etc.
One might also be tempted, as Sartre does, to universalize this into a general principle, that for virtually any action that satisfies the categorical imperative from one direction, it will be found to violate the categorical imperative from another (this is, in a sense, just what it is to be "thrown into the world"). The result of adopting this principle is much stronger, since the result is that the set of actions endorsed by the categorical imperative will end up empty. On Sartre's view, it's not just that the categorical imperative will end up leaving some right actions out. Rather, the categorical imperative is incapable of determining action at all. Sartre diagnoses this problem by saying that the categorical imperative is too formal to determine action a priori.