This is done by paying selective attention to them. That is, you pardon and excuse (or even ignore) the ridiculous gaffes made by yourself and your allies, while excoriating your opponents for theirs.
(This is a common bias: people tend to focus on the flaws and mistakes of those they hate, while casting a blind eye to the flaws and mistakes on their own side.)
Under the "Examples and Analysis" section below, you will find a list of gaffes made by different people of different political persuasions. Consider how these gaffes were put to use, how they were treated by different people. Some people pointed to them as evidence of extreme stupidity, ignorance, obtuseness, etc., while others excused them as merely a "slip-up" or ignored them altogether.
EXAMPLES AND ANALYSIS
"You all have friends thinking about voting for Donald Trump. Friends do not let friends vote for con artists. All right, so you want to have a little fun? All right, what is Donald Trump do when things go wrong? He takes to Twitter. I have him right here. Let's read some. You'll have fun. All right, number one, here's the first one, "Lightweight Marco Rubio was working hard last night." This is true. "The problem is, he is a chocker. And once a chocker, always a choker." I guess that's what he meant to say. He spelled choker, C-H-O-C-K-E-R, chocker. He called me Mr. Meltdown. Let me tell you something, during one of the breaks, two of the breaks, he went backstage, he was having a meltdown. First, he had this little makeup thing applying, like, makeup around his mustache, because he had one of those sweat mustaches. He wanted a full-length mirror. Maybe to make sure his pants weren't wet. I don't know. Then I see him pacing back and forth, and then he is huddled in the corner talking to somebody, waving his arm up and down and the person trying to calm him down. Any way, but I'm a chocker. All right, next tweet. "Leight weight chocker, Marco Rubio, looks like a little boy on stage, not presidential material." He meant to say lightweight, but he spelled it L-E-I-G-H T, so he got it wrong. "Looks like a little boy on stage." It's not that I look like a little boy, it's not that I would be the youngest president but he would be the oldest president ever elected. So you start to worry. All right, last one, "Wow, every poll said I won the debate last night." Now, this is him about himself, OK. "Great honer." I think he meant to say "honor." I don't know how he got that wrong, because the "E" and "O" are nowhere near each other oh there on the keyboard. That's what I'm thinking. So how do this guy three tweets misspell words so badly? I only reach two conclusions. Number one, that's how they spell those words at the Wharton School of Business where he went. Or number two, just like Trump Tower, he must have hired a foreign worker to do his own tweets. All right, so guys, we have a con artist as the front-runner in the Republican Party. A guy, a guy who has made a career out of telling people lies so they come in and buy his product or whatever he does. You ever heard of Trump vodka. You have? Well, it isn't around any more. Or a Trump mattress, or Trump air, or Trump ice or Trump water. Those are all businesses that are gone, because they were disasters. Trump hot air, yeah."-- Republican presidential contender Sen. Marco Rubio (R-FL), February 26, 2016, referring to Republican presidential contender Donald Trump.
Comment: Rubio is mocking Trump for his gaffes, as well for Trump's mocking of Rubio. It's not clear how much (if any) of this is meant comically.
[Rep.] Alan Grayson [(D-FL)] is Elizabeth Warren without a filter — but he intends with her help to become Florida’s great Democratic hope. Since Grayson first burst onto the national media scene as a first-term congressman from Central Florida with a savage wit, he has generated near non-stop headlines and Internet hits, calling all manner of political opponents “whores,” “vampires” and “knuckle-dragging Neanderthals.” Even some Democrats who agree with almost all of his policy positions want to keep their distance. … After he shot into the national media arena in 2009, Grayson was unbowed, asking me, “Is it a necessary element of this job that I take shit from people? No one gets a free pass if they attack me. I don’t think it’s beneficial to turn the other cheek. There is no reason a Democrat has to be a weakling.” … His strident criticism of the financial system led to an early — and highly embarrassing — gaffe in February 2010, what soon would become just an indicator of what was to come. In a radio interview, Grayson attacked Linda Robertson, a senior adviser to Fed Chairman Paul Bernanke, calling her a “K street whore” and accusing her of “trying to teach me about economics.” He later apologized. Yet once catapulted into the national spotlight for his outrageousness, he never looked back. In fact, he doubled-down, comparing former Vice President Dick Cheney to a vampire bat (“I have trouble listening to what he says sometimes because of the blood that drips from his teeth while he’s talking”), calling the Republican Party a “lie factory” and dubbing Rush Limbaugh a “a has-been hypocrite loser” who was “more lucid when he was a drug addict.”-- From an article in Politico, May 20, 2015, by Mark I. Pinsky.
Comment: What Pinsky calls a "savage wit" and "gaffe" on the part of Grayson is better described as demonizing. "Whore" is name-calling of the "sexual deviancy" sort. Also, Grayson reportedly uses "get tough" rhetoric, according to Pinsky.
U.S. Rep. Loretta Sanchez has apologized for an ethnically touchy gaffe that was caught on cell phone video.-- From a CNN article, May 17, 2015, about remarks made by Rep. Loretta Sanchez (D-CA), on May 16, 2015.
The Democrat, who is running to replace California's retiring Sen. Barabara Boxer, would otherwise seem like a paragon of diversity. But when she let out a stereotypical Native American "war cry" over the weekend, it marred that image and sent her running.
Literally -- away from a reporter trying to chase her down for comment on the gaffe that many found racially offensive. But late Sunday, she spoke about the slip-up.
Native Americans know she's watching out for them, she said at a Democratic Party convention in Anaheim, as reported by the Los Angeles Times. "And they know what many of you don't know — that like so many Mexican Americans, I am proudly Native American on my mother's side," Sanchez said.
Sanchez was ad-libbing at a California Democratic party convention in Anaheim, when she made a stereotypical Native American "war cry."
Raising her hand to her lips, she let out about two seconds of it.
"I'm going to his office, thinkin' that I'm gonna go meet with woo-woo-woo-woo, right? 'Cause he said 'Indian American,'" she said, using the gesture to try to discern between Indian Americans -- with ancestry from India's subcontinent -- and Native Americans.
Comment: Were Sanchez's remarks a "gaffe" or a racist slur?
Examples from 2013.
Examples from 2012.
Examples from 2011.
Examples from 2008.
OLBERMANN: As we continue -- scrap NAFTA, Senator Obama, or fix it?-- Sen. Barack Obama (D-IL), August 7, 2007, during Democratic Party presidential primary debate moderated by Keith Olbermann.
OBAMA: I would immediately call the president of Mexico, the president of Canada to try to amend NAFTA because I think that we can get labor agreements in that agreement right now.
Comment: Canada has a prime minister and a governor-general (who is the representative of the British monarch), but no president.
Examples from 2000.
"A minor slip-up by Vice President Dan Quayle hatched a frenzy and a long-running joke. Quayle led a spelling bee for sixth-grade students while visiting an elementary school in New Jersey in 1992. Working from an inaccurate flash card prepared by a teacher, he corrected William Figueroa, 12, when the child spelled "potato" on the blackboard -- making the boy add an unnecessary "e" at the word's end. Quayle would never hear the end of it."-- Account of incident involving Vice President Dan Quayle that occurred on June 15, 1992.
Comment: This gaffe was partly due to the misspelled flash card -- which spelled the word "potato" as "potatoe" -- made by the teacher, but also due to Quayle's failure to catch the error.
(The list above is not intended to be a comprehensive record of all relevant examples.)