Every now and then I'll write a lecture on this topic. I find it somewhat interesting, and apparently there aren't too many other authorities on the subject with which to compete... Plus, it's all pop-culture opinion so its not like I can be yelled at for not following good academic procedure. (Academics sometimes forgets about pop-culture.) Which basically means I'm free to give my educated bullshit and you can take it or leave it.
Saturday Night Live is a show of punctuated equilibria. It has to be. There is no other way a show like Saturday Night Live could last this long otherwise. There are two major types of SNL casts: equilibrium casts and transitionary casts. Everyone usually remember the good equilibrium casts, but the real importance is in the transitionary casts.
The equilibrium casts are when everyone "gels" for the most part and the humor works. A good equilibrium cast has their humor rooted in the present. This is an obvious requirement, as it keeps the show rooted. But, as obvious this is a requirement, people often forget the consequences of this requirement: No cast can remain forever (their humor and group dynamic are rooted in a particular time and become stale), and people become attached to equilibrium casts. The former is the more obvious consequence, whereas the latter is a more indirect consequence... Basically, people set down roots in years as well and those roots can lead to nostalgia and ties with the equilibrium casts of the same years.
There are people who have strong ties to the original cast. My parents continue to watch SNL to this day, but will often reminisce of the original cast from their college years. I myself felt that pull and almost stopped watching SNL at the end of the late 80s/early 90s equilibrium cast (the Carvey/Hartman/Farley/Myers/Sandler cast) that I grew up with. But I stayed, and I liked the late 90s equilibrium cast too.
However much people love the equilibrium casts, it is the transitional casts that keep SNL alive. The transitional casts evolve the show, as they can often experiment where audiences might not have permitted their "friends" in the equilibrium to. (Eddie Murphy and Martin Short's famous stints on SNL were both transitory in nature.) The transitional casts keep the show running (who would watch SNL if it was taken off the air every five years or so?). The transitional casts form the foundations of equilibrium casts. This last is important; go back sometime and watch the transitional years of your favorite cast, they can be eye-opening how subtle annoyances would be worked out and subtle charms focused upon in later seasons.
This current cast is transitory. It's a group of people, each funny in their own right, trying to establish a good group dynamic that can entertain people, and connect with audiences. I would say this cast really had much of a chance yet to "gel", but I'm hoping to see good results from them in another season and a half or so. First of all, I don't think they quite started to get enough spotlight until Papa Ferrell (love him or hate him) left two and a half seasons ago. Then the usually likeable Sandler Lite (Jimmy Fallon) a first-out-the-gate star, and one of the cornerstones of the transition cast left. This leave slowed the transition some.
Ultimately however, and unlike in some of the previous transitions, the cool thing about this transition is that even if there haven't been as many "good characters", there has been a very steady and firm hand on the till of the writing, Tina Fey. To say that Tina Fey has been trying to make steak out of bad ground beef, is a poor analogy. It's really just that Tina Fey has been trying to make a group of comedians that just met at most six years ago (when Fallon, Parnell, and Sanz joined) and as recent as last season (Finesse and Nickolodeon Alumnus Thompson) appear to be good and fast friends that have known each other all their life. It's a community thing, and building communities is a tough thing to do. To make it seem to work as well as it has this season when its been good has to have taken a lot of skill, and I would very much believe that Tina Fey is paying a lot of attention to each comedian's skills and weaknesses in order to pull it off.
The result is that this transition cast hasn't been hit hard by the "SNL is being cancelled" rumor that has dogged some of the earlier transition casts (which I saw between the early 90s (eq.) cast and late 90s (eq.) cast, and have heard about in the previous years, from books).
On the other hand the biggest problem right now is the "OMIGOSH, SNL IS BEING LED BY A WOMAN!" shouts. The current cast is the most diverse SNL cast yet, and there seems to be some currents of sexism and racism amongst the people talking about how much the current SNL sucks. The other thing is that SNL, as it does when it does best, is following the cultural zeitgeist and is being very "People"-like in an overt pop-culture vulture way. However, its very much due to the rest of the current culture being fixated on it (MADtv has stayed almost exclusively in pop culture and out of politics). Not to mention Tina Fey is a very dry and layered comedian, and its hard not to believe (or feel) that overall a lot of the pop-culture-mania is wrapped in several layers of satire and sarcasm, at once both self-deprecating and acknowledging. (Just as Mean Girls was both extreme satire and interesting emotional lesson.)