Trevor Noah in 2009. (Bongiwe Mchunu/The Star via Associated Press)

Just a day after Trevor Noah was welcomed by some as an exciting new choice to host “The Daily Show,” the South African comedian, who is little-known in the United States, has come in for criticism as writers and fans have begun to pore over his body of work. The biggest target has been the archives of Noah’s Twitter feed, where he tried out material that targeted Jewish women, heavier women, Jews and Israel.

What connects the tweets that have landed Noah in hot water is less that they represent political offenses of the same magnitude than that they’re all embarrassingly awful jokes. Riffs about fat chicks are the stuff of schoolyards. Even Judd Apatow movies stick with implied shiksa humor rather than jokes about Jewish women. And at least one of Noah’s jokes about Jews and Israel — a tweet about almost accidentally hitting a Jewish kid while driving a German car — seems more like a Justine Sacco-style inept joke about anti-Semitism than an actual biased quip. (The others show even less sophistication.)

It’s rare to see an incident that unites so many constituencies in shared ire. And while it remains to be seen whether Noah can dissipate all these objections at once, a possible solution to at least some of his problems might lie in another controversy about “The Daily Show.”

It’s striking to compare the sheer cheesy badness of Noah’s old Twitter jokes with the great riff on an old chestnut that “The Daily Show” used to introduce him on his first appearance:

The tweets rely on the idea that simply invoking “fat chicks” or Jewish influence is funny. The “Daily Show” bit is transformative, taking the “I just flew here and boy are my arms tired” into something much more provocative. It’s not just the distance Noah traveled that has exhausted him; it’s the social customs he encountered on his arrival. The other difference, of course, is that while Noah was presumably writing his own tweets, when he appeared on “The Daily Show” he had the support of the show’s writers.

It’s worth remembering that the last time “The Daily Show” was the object of this much criticism, it was back in 2010 when Irin Carmon shined a spotlight on the franchise’s difficult history with female correspondents and women writers. The problems existed under both Craig Kilborn, who was suspended for remarks he made to a magazine about the sexual availability of one of the series’ creators, Lizz Winstead, and his successor, Jon Stewart, who had trouble recruiting and keeping female corespondents and writers. The numbers have gotten somewhat better over the years. In 2009, “The Daily Show” had two female writers. When Noah made his debut on “The Daily Show,” that figure had climbed up to four, although women were still in the minority.

A partial solution to Noah’s current quagmire may lie in his predecessors’ woes. Before people started digging into Noah’s Twitter feed yesterday, NPR’s Linda Holmes noted that Noah’s arrival in the anchor’s chair may shift the perception of the show from “a pure expression of Stewart’s sensibility” to a more writer-focused enterprise.

“With Noah being so much younger and newer to the scene than Stewart has been for many, many years — and so much less familiar to much of the audience — we may see a shift toward the show being treated as less of a tour de force and more of a collaboration, which probably represents it more honestly, particularly while he’s getting himself established,” Holmes wrote. “Speaking of writers, it will be interesting to see whether the existing writing staff sticks around without Stewart. Having to populate that writers’ room with new people would represent both a huge challenge and a huge opportunity.”

Noah should take that opportunity. At some point, he’ll have to answer to critics of those tweets and explain how he has grown as both a comedian and as the progressive political thinker he claims to be. When he does, he should pair that narrative with real action, explaining what kind of writers and correspondents he wants to surround himself with and what he hopes to learn from them. If Noah’s big selling point is that he offers a fresh perspective to the audience for “The Daily Show,” then he should demonstrate that he values the same thing in his own staff.

Hiring more women and people of color on “The Daily Show” probably won’t satisfy everyone who’s angry at Noah today and who is hitching up the bar he’ll have to clear to be a success at his new job. But more than taking back some lame jokes, it would be a substantive step toward making “The Daily Show” embody its own values.