yes you can concense lots of liq. O2, if there is significant leak (= very poor vacuum) and air flows through the system. I have done it twice, by accident. Oxygen has higher boiling point than nitrogen and will condense in trap cooled by liquid N2 - you will see light blue liquid. This is very dangerous as the contact of organic residues with liq. O2 can cause explosion, especially from mechanical provocation.

If this happens, the right way to deal with it is not to try to take the cold trap apart - it only increases the chances of explosion. You put a blast shield in front of the cold trap filled with liq. oxygen, leave the pump running overnight, try to stop the air leak (if you know where is it coming from) and notify the other lab members about the problem. The situation resolves itself overnight, as liquid nitrogen in Dewar expires, the whole thing warms up and oxygen is in the trap boils off into the pump that is left running.

Also, if you are using liq. N2 for cooling your cold traps, you must make sure they are clean and dried before use.