On a separate note (or possibly related), I just couldn't get into this show. I love Stewart and watched daily show for years. I found the problem with... Problem was that it had a fear that the content wasn't good enough to stand on it's own so there was this constant barrage of quips that frequently fell flat. Maybe the show got better over time (I only caught the first 3 or 4 episodes).
The Daily Show was mostly upbeat and highlighted the absurdity of politics even when they were covering serious topics, so the jokes seemed to flow pretty naturally. In The Problem Jon Stewart would oscillate between serious/morose to a few jokes and back again, it was giving me thematic whiplash and I couldn't hang with it either. I think Last Week Tonight is The Daily Show's spiritual successor.
Man have you not watched last week? Morose and serious is like how I would define it. Oliver even made a joke last week about how 'if I'm talking about something it's probably horrible and tragic'.
I think this all goes to show tone shifting is a difficult art and artists who choose to do it need to be able nail it or get ready to fall flat. I think Oliver is a master at tone shifting and it's all done with taste and confidence.
Jon Oliver is very careful to segregate jokes for levity from sensitive topics. Jon on the Problem would regularly never make a tonal or topical shift when putting in a joke, which really made it feel like a desparate, uncomfortable interjection during a serious rant rather than a lighthearted reminder that we're still on Earth while discussing a travesty.