At the beginning when Barney is playing the piano he has a cigarette in his mouth. You see him put it out in the ash tray, he has a scene with Ethel Barrymore and then when the camera cuts back to him playing he still has the cigarette in his mouth.
When Laurie asks Barney why he doesn't have any plants in his window box, he says because they use up all the oxygen. People commonly conceive that plants actually use carbon dioxide and produce oxygen, and this has therefore commonly been regarded as a goof. However whilst a plant is a net producer of oxygen, it does this mostly during the day, whilst it is photosynthesizing, at night time plants do indeed use more oxygen than they produce and this can affect sleep. Barney's explanation is therefore quite sophisticated and indicates a focus on the night time.
When Day and Sinatra are icing the gingerbread men/persons, they refill the icing gun, but the icing is added on top of the plunger.