In the scene where Miranda is woken at 4am by the puppy whimpering to go out, Miranda enters the hallway and picks up the puppy who is rather large in size. In the next scene when Steve walks in the door some hours later the puppy comes to greet him and it is much smaller than the one Miranda had held in the previous scene.
When the waiter serves the wheatgrass shots to Samantha and her date, both shots are full to the brim; however, when Samantha raises her shot to her lips it is no longer full to the brim.
When Carrie is typing on her laptop she says "women tend to use the left, more emotional side of their brain, and men the right, more logical side". It's actually reversed, with the left hemisphere generally thought of as more logical (it processes language), and the right as more emotional (it processes images).