In the scene at Amy's apartment, Oscar serves champagne in two glasses: one green and one crystaline. When Amy gets out of the shower, Oscar hands her the green glass. But in the next shot, when Amy and Oscar make a toast and lift their glasses, the glasses have been switched: Oscar holds the green glass and Amy the crystaline one.
When Oscar has finished giving the speech, Amy gets out of her seat. In the next shot, Amy is sitting while everyone is still clapping, then she gets up and walks out.
The taxi cab Amy and Oscar take after leaving the restaurant (where they ate the tuna melt) changes from a newer model car they pulled over (and whose handle they broke), to an older boxier model in the cut scene with them driving away in the rain, then back to the same newer model they pulled over in the first place.
When Oscar makes dim sum for his friends he criticizes Rick for putting ketchup on the spring roll. When the shot widens out, there is no ketchup anywhere near Rick.