A certain amount of tension always precedes a “Saturday Night Live” season premiere, but this weekend’s curtain-raiser, kicking off its 45th year, seemed tenser than usual.

Beyond the typical curiosity about how the show would shake off the cobwebs of its annual summer hiatus and whether new cast members would gel with the veterans, “SNL” had two big questions to answer: How would it tackle a politically tumultuous week in which Speaker Nancy Pelosi announced that the House would begin a formal impeachment inquiry against President Donald Trump? And how — if at all — would it deal with the controversy surrounding Shane Gillis, who was hired as a featured performer and dropped before the season started, after videos surfaced in which he used racial slurs and other bigoted remarks?

The first question was addressed right away in the show’s cold open. Despite his frequent grousing to the contrary, Alec Baldwin was back in his recurring role as Trump, placing an anxious phone call to his personal lawyer, Rudy Giuliani (played by Kate McKinnon). “Nobody’s going to find out about our illegal side dealings with the Ukraine,” McKinnon assured him. “Or how we tried to cover up those side dealings. Or how we planned to cover up the cover-up.”

Baldwin asked her, “Rudy, where you right now?”

“I’m on CNN right now,” McKinnon answered.

As is “SNL” tradition, a series of cast members appeared in subsequent phone calls as members of the Trump administration and its associates: Aidy Bryant as Attorney General William Barr; Beck Bennett as Vice President Mike Pence; and Alex Moffat and Mikey Day as Donald Trump Jr. and Eric Trump.

“Did you take care of that thing in Russia for me?” Baldwin asked them. “What thing in Russia?” Day said. “The treason,” Moffat replied.

Bowen Yang, a new featured performer, appeared as Kim Jong Un of North Korea, who offered Baldwin his advice on how to deal with the whistleblower. (“You have a big ocean in your country?” Yang asked. “OK, send whistleblower to the bottom of there.”) After further appearances by Chris Redd as Kanye West, Kenan Thompson as Don King and Cecily Strong as Jeanine Pirro, Baldwin found himself in a final conversation with actor Liev Schreiber.

“I told you, Mr. President, Ray Donovan’s a fictional character,” Schreiber explained to him.

Baldwin replied, “If you can’t do it, can you connect me with John Wick?”

Mea culpa (or was it?) of the week

While “Saturday Night Live” has a history of using its own airtime to acknowledge and apologize for its missteps, the show did not take on the Gillis controversy directly. But in his opening monologue, the host, Woody Harrelson, obliquely addressed its subtext — whether intentionally or not — in a riff about immigration, cultural sensitivities and comedians who are constantly called on to say they are sorry.

After a few jokes about his unexpected status as a “fashion icon,” Harrelson said, “I wasn’t born yesterday. I didn’t just get off the boat. Oh, jeez. That’s ironic. That sounds like I’m slandering immigrants. I’m not. I think immigrants make this country great. But let’s face it, most of them, they don’t come by boat anymore. They just walk right in. We see that every day on the news. Well, Fox News anyway. Oh, jeez. If what I just said offended Fox News viewers, I apologize. And if I hurt the one Fox viewer who is also an immigrant, well, I apologize to you, madame first lady.”

And so on, through a series of equally awkward faux gaffes and apologies.

Other Political Sketch of the Week

A segment billing itself as a CNN town hall on impeachment offered another opportunity for the “SNL” cast to try out or refine their impressions of Democrats seeking their party’s presidential nomination in 2020: a first wave included Moffat as Beto O’Rourke (“Can I say a few words in 8th grade Spanish?”); Yang as Andrew Yang; Redd as Cory Booker; Colin Jost as Pete Buttigieg; and Chloe Fineman, a new featured performer, as Marianne Williamson.

A second, more star-studded round focused on Kate McKinnon as Elizabeth Warren (“I hope you guys enjoyed hot girl summer, ‘cause now it’s school librarian fall”); Larry David as Bernie Sanders (“I’m so excited to be back and to ruin things a second time”); Harrelson as Joe Biden (“I see you, I hear you, I sniff you, and I hug you from behind”); and Maya Rudolph as Kamala Harris (who described herself as the kind of fun aunt — “a funt” — who “will give you weed but then arrest you for having weed.”)

Other-other political sketch of the week

A political roundtable parody hosted by Bryant made use of flashbacks, costume changes and the unshakable pessimism of a panelist played by Thompson to consider the likelihood that, for all the firestorms that Trump has faced, “Ain’t nothing going to happen,” as Thompson’s character puts it. (The sketch was also distinguished by the accidental on-screen appearance of a person helping to change Bryant’s costume, after which the actress broke character and couldn’t stop laughing.)

‘Weekend Update’ jokes of the week

At the “Weekend Update” desk, anchors Jost and Michael Che continued to riff on the impeachment inquiry into Trump.

Jost said, “This week, President Trump was accused of a shady, mafia-style shakedown of the Ukraine. But luckily Trump’s lawyer was able to smooth it over with professionalism and class. [Video plays of Giuliani on Fox News, telling other guests to shut up.] By the way, that looks like the world’s angriest game of Guess Who? And now Democrats are moving towards impeaching Trump, which should feel like a huge, historic moment. But with Trump, even impeachment just feels silly. Like, the movie ‘Nixon’ was a serious film directed by Oliver Stone. The movie about Trump is going to be from the dudes who brought you ‘American Pie.’ And by the way, the one thing we haven’t heard from the White House all week about this is a denial. Trump just keeps saying that all the information is bad because it’s secondhand. It’s like if the cops asked you if you murdered someone, and instead of saying, ‘No, I didn’t,’ you said: ‘Who told you that? Ron?’ ”

Che, after noting his frustration at how long it would take to remove Trump from office, added: “I bet somebody explained how long impeachment takes to John Wilkes Booth and he was like, ‘OK, well, where’s he at right now?’ ”

Fake Movie Trailer of the Week

If you had any lingering curiosity about seeing the “Downton Abbey” movie, this satirical trailer will suck it right out of you. The “SNL” parody features a close approximation of the sumptuous production value seen on the TV series and in the movie (as well as McKinnon’s dead-on impression of Maggie Smith). But, as a voice-over informs us: “The beloved television show is now a feature film. And it’s mostly about cleaning.”