I felt like there was actually a lot of plot I missed (because I'm always far more interested in watching the character interactions)

Yeah, that happens to me, too! I'm really character-focused when I watch TV or theatre or anything, so I don't always register the plot bits properly in my head. I suspect this may be one of those that when you watch it more times, the logic holes become more apparent, but I still enjoyed it. :-)

(Sorry for the delayed reply, my brain's not been great at focusing recently.)