the Abridged Series "genre" is dead. It peaked with YGOA and DBZA. N other reached even half the notability those two had.
That said, abridged series suffer from the same problem most 00s comedy had, and that's two main traits: One, writers figuring out that it's suddenly okay to lampoon your own genre, but they usually did it so by having the characters loudly pointing out the clichés in lengthy spiels clearly directed at the audience; basically, explaining the joke BEFORE telling the joke in an attempt at appearing smarter than anybody else. And always with that awkward, weirded-out tone.>"Wait, hold on, I-I-Im sorry but, you're saying that [describes trope here]? How does THAT make sense, huh?! HUH?!"
And two, excess of non-sequiturs. I might be alone in this one, but after replaying quotes from Portal, I noticed how dated the humor can come off. Especially in that DLC where it was only Cave Johnson and featured JK Simmons going in speedy rants about ridiculous stuff in one breath while acting as if everything's normal. I think that's very 00s. Like some turn-of-the-century version of Monthy Python, except more wordy.
Those are just my impressions. I think a /co/-related work that really captures the 00s essence (and dateness) is Kim Possible.