It was a risky strategy for “Saturday Night Live” to put on a star-studded 40th-anniversary special. Seen from the wrong angle, it could make NBC’s late-night warhorse look like a museum piece, instead of a still-vital part of the TV — well, OK, maybe the special makes sense.

“SNL’s” company in the TV longevity race, after all, includes the likes of “60 Minutes” and “Meet the Press.” And just for the record, the actual 40th anniversary of what was truly groundbreaking television doesn’t come until October. So maybe there’ll be a rerun then, for accuracy’s sake?

Certainly Sunday’s 3½-hour live festival of celebrity cameos and Studio 8H self-indulgence did an awful lot of recalling past glories: One quick-snippet clip reel after another proved that punchlines need a setup and that medleys always are the sad part of an aging singer’s concert.

Eddie Murphy, in a much hailed return to the “SNL” stage, reminded us, sadly, that Eddie Murphy has probably had the movie career he deserved.

The show provided a fair number of laughs, to be sure, amid not nearly enough new material. This is “Saturday Night Live,” and those of us who have decried the show in one season or another tend to forget that, from the outset, its signature characteristic has been unevenness. “SNL” has ensconced itself as America’s favorite hate watch — or its most despised love watch. The balance changes from season to season, from host to host, from sketch to sketch. But it’s never just one emotion.

So Bill Murray’s lounge-singer rendition of the theme from “Jaws” — a sequel to his early-days theme from “Star Wars” — was the highlight of the evening; he’s terrific as an actor playing all the variations of morose, of course, but he’s also a pretty great, fully committed sketch comic.

Steve Martin, in the opening monologue, reminded us why he became Steve Martin: So crisp, so sharp, so dry — and even willing to play along by reprising his 1970s pop hit “King Tut.” Take note, Eddie Murphy.

A new digital short, the power ballad “That’s When You Break,” made effective fun of all the laughing cast members have done within scenes. The mock soap opera “The Californians,” of recent vintage, still worked with an update featuring Bradley Cooper as a new pool boy and Betty White playing, what else, a randy old lady.

Having Jane Curtin join Tina Fey and Amy Poehler on the “Weekend Update” anchor desk was inspired, as was Fey’s joke saluting “one of the show’s original producers, cocaine.” Listing the still extant Jon Lovitz among the show’s dearly departed was a fine running gag.

But, again, unevenness.

On a supposed big event like this, does Miley Cyrus really deserve to sing a full song (Paul Simon’s “Fifty Ways to Leave Your Lover,” which she mangled with odd fakey voices)? At least longtime friend of the show Simon, who got to close the night, didn’t have to do it with a Cyrus song. (He sang, touchingly, “Still Crazy After All These Years.”)

Were “Mom Jeans” and “Colon Blow” and Dan Aykroyd’s “Bassomatic” the ads and sketch deserving of full reprises? (OK, maybe “Mom Jeans.”)

As for Murphy, he said being back there was like being back in high school, which must mean that in high school he held himself aloof and didn’t try very hard. Arguably the funniest cast member the show has ever had — which is saying something — Murphy inspired Chris Rock’s highly engaging, how-great-thou-art introduction. But the man himself tossed out a few platitudes, then went awkwardly to commercial. Sigh.

He was right, though, about the reunion bit. Past hosts who returned included Alec Baldwin, Justin Timberlake, John Goodman, and on and on and on. Past cast greats included Dana Carvey, Norm MacDonald, Will Ferrell, Kristen Wiig, Aykroyd, Bill Hader, and on and on and on. You knew a lot of people had shown up because the opening credits were even longer than the credits for regular editions of the show. Which is also saying something.

What’s funny is that the 2014-15 edition of “SNL” has actually seemed to be on an upswing. There’ve been more good videos and a higher proportion of sketches that seem to have dramatic shape and at least a modestly sharp point of view. You probably disagree; this is how “SNL” keeps us going.

But the special, in the end, doesn’t feel like it’s going to be a key part of the legacy.

Except in its efforts to hammer home the idea that “SNL” has been central to pop culture — which we already knew — this, really, did not feel like a show for us. With all the famous friends it kept displaying, it seemed more like a prelude to a pretty exclusive after-party. We hope they had fun, and that it didn’t drag on for 3½ hours.