As I understand it, there are three standard arguments against behaviorism:
1) The argument of Chisholm (1957) Peter Geach (1957) based on the holistic nature of mental states; how one reacts to a certain stimulus may depend on several beliefs and desires one has.
2) Chomsky's (1959) argument based on the "creative" or "productive" nature of language, and the inability of behaviorism to account that.
3) Putnam's (1965) argument based on unmanifested mental states (e.g. "superspartans" who never show they are in pain...)

Best, Panu