An important problem is that CRC cards do not help people distinguish the concept of class and object. This is especially bad for the beginner.
The freedom of the CRC technique often means that the distinction between class and object is blurred. Especially in later role-play, having two objects played by the same person with the same card can cause learners to lose the distinction.
Because many systems involve singleton class, where there is only one object in a class, the need for separate object and class names seems a confusing irritant to beginners.