I'm kind of inclined to agree with the sentiments of people like Frank Oz, Joey Mazzarino, and such.
From Frank's perspective (and even others like Caroll Spinney, Ken Diego, and the like), one of the things that made SS so special back in the day was the camaradery among the cast and crew - you really felt like everybody was a big family, they really were your neighbors, and they felt like real people who really cared about each other . . . that did carry on for decades, but in recent years, as older people have left us for one reason or another, and other factors have been brought into play (such as dwindling the number of cast members), that sense of camaradery has weakened, and there really isn't much chemistry or a sense of family anymore. Not to mention, as people like KarWash and others have pointed out, the human actors feel less like themselves, and more like quirky kids show personalities: the Alan of today feels nothing like the Alan of the late 90s and early 2000s, even though he's still Alan Muraoka.
The other thing, I feel, from both Frank and Joey's perspective is SS has lost quite a bit of its charm as it tries harder and harder to compete in the ever-growing world of pre-school entertainment. Of course, it continues to keep up with the times, culturally speaking, but there's definitely a lack of "hipness" (as Frank has said) that actually made it appealing, and I'm inclined to agree with Joey that the drastic cutback on parodies, sly writing, and the like have really made SS lose its heart and soul. Yes, it was always a kids show, but the parodies and the bits/sketches/inserts that were written in a way to help offer older audiences with humor they could understand without it being inappropriate for kids is what really helped make the show what it was . . . without that, it feels like almost any other ordinary kiddy show. That, and to, as Shane has pointed out multiple times, there's really no substance to street stories anymore: they rarely have any actual engaging plot structure anymore, and they're, more-or-less, "random things happening" with some educational content thrown in.
To me, this is how and when SS has gone downhill.