In general I think it's pretty easy for a DLM to turn a bit awkward. When you've got that many people together & you're playing a game where there are varying levels of giving a shit, there is bound to be tension. Sometimes I find it hard to finish one, but only because I get flashbacks to family games of Monopoly & Trivial Pursuit gone dark.
Two podcasts that really stand out to me (that haven't been mentioned) as being awkward are the CBB with Will Forte. Before PFT arrives it seems like Will Forte shuts down every time Scott tries to riff too much. I remember a good 10 minutes of Will Forte just talking about how great the director of Nebraska was, and how nervous he was to do a serious movie, punctuated by Scott trying to make some jokes that Will Forte just moves right along from. I like Will Forte, I think he just wasn't sure what was going on or he just really wanted to talk about Nebraska. It really picks up for everyone once Richard Harrow is on the scene.
Then also the WTF with Annabelle Gurwitch & Jefff Kahn. The two of them are married and they seem to really hate each other - at first it seems like a playful albeit awkward schtick, but eventually it seems to just devolve into the kind of barbs you see between a couple the night before a murder-suicide. Call me a softie, but it made me really unhappy. Marc tries to play along with them but sometimes it seems like he feels uncomfortable too, and that's saying something. Also, more pube talk than I can handle. I hate when Marc talks sex, those Adam & Eve ads used to make me feel so uncomfortable.
My first podcast I ever listened to was actually the WTF with Gallagher, so I have a lot of affection for the awkward ones.