I'm not sure if this quite fits what you are looking for, but certainly a good example of the limits of cooperation would be Soviet internment of Allied fliers who were involved against the war with Japan, which I write about here. I wouldn't exactly call it an attempt to put one over on the USA, as there was international treaty obligations in play, and the Soviets did eventually allow some bending of the rules in any case, but it certainly helps paint a picture of how imperfect an alliance it was, which I think is what you are mainly after here.

While it may be difficult to describe as a specific event or incident, the Soviets did conduct espionage on the Manhattan Project. u/restricteddata has written on this subject in:

Eric Schlosser says the USSR's first nuclear weapon was almost identical to the one used on Nagasaki because a 'network of Communist spies' at the Manhattan project 'simply took' the plans. Was the US atomic program really this compromised?

This thread from his AMA on the Manhattan Project

How much did Stalin know about the Manhattan Project?

How much did the Soviet Spies in the Manhattan Project contribute to its success?

How did the Soviet Union manage to spy on the Manhattan Project?