Yeah, I had a similar experience with Sopranos which made me to go back and watch the entire thing with a bit more air between the episodes. I'm not saying you have to wait a whole week for each episode, but there are certain things you'll inevitably rush past if you watch an entire season in the span of a few days.
I find it interesting how many of these shows incorporate the pacing of everyday life into the experience. The processing between episodes becomes important for the temporal space in which the story exists to make sense. Particularly in shows like The Shield in my opinion, where we walk next to these characters for a very long time. We actually get to experience Vic Mackey's fall from grace as it happens. Season after season the reality of Farmington slowly begins to overlap with our own. It becomes a second everyday life that we return to now and then. The documentary like cinematography and the shaky footage in the show just adds to this feeling. I remember thinking it was bloody annoying during the first season but it really serves a larger point. Most of the aesthetic decisions do. It's ultimately what makes it so great. The Shield asks for a fair bit of patience in return though, and a lot of the viewers won't give it the time it needs to grow, which means that many of them will only latch on to the broader themes and storylines. The point of modern television compared to film is depth.