If you're wondering about whether a cartoon has aged well and you find it hasn't, it may be because you've aged, period. I mean, it's hard for me to sit through an episode of Masters of the Universe, but my niece loved it when I showed it to her four years ago. But she'd probably have a hard time watching it now, too.
My problem with the newer Looney Tunes stuff (seriously, I liked Merrie Melodies shorts better on the whole), not just the Show but everything in the past twenty or thirty years, is that they really don't know what to do with the characters. They're always archetypes: Bugs is the snarky lead; Daffy is the foil/fool. Porky is the second fiddle relief. In the old shows, they were really whatever the hell they needed to be. In a lot of cases, you could plug most any character in that script, which has its own pitfalls but you also don't pigeonhole your cast to a type. And there was a sophistication that only the better modern cartoons have (which is due to the largely adult audience they played to, but still).