This is a straight continuation of the first season: while that one doesn't have any closure, the second one doesn't have any introductions -- so it's best to watch them back-to-back (or at least reasonably close together, while it's still fresh). There's not much plot development in the second season either, though the focus shifts slightly more to Rec's life at the bridge and away from his 'previous' life.
There is one major character introduced, who turns into a romantic rival for Nino -- that, and some other issues pop up that deepens Rec's understanding for Nino (and vice versa). Still, it's not like their relationship shows any progression at all.
The zanyness is turned up a notch or two in this season, with some situations straying into bizarre territory (to which Rec remarks: "OK, we'll just pretend we're daydreaming right now, right?"). While it keeps being funny, it also shows that 'normal' life under the Bridge has been milked for all the gags that are in it. I'm not sure a third season would work.
Quality-wise, it's the same as the first season. My guess is that the animation team simply continued on with the second season straight after the first one. Of course, there are new opening and ending themes -- suitably bizarre songs, which I liked.
If you liked the first season, you will like this one too -- because it's more of the same, without getting boring. I'll give it a 7.
Also, there's a live-action drama series under production at the moment. I'm not sure how that would work out.