The main flip between this depends on whether they're debunking people who are accidentally (or intentionally) using faulty scientific claims and/or simply don't understand the subject, and when they're talking about things that, to a degree, boil down to little more than opinion and cultural values.
There are three main positions they argue from: skepticism, atheism, and libertarianism (both social and economic). Since, in America at least, the first two are associated with Liberal politics episodes dealing with the third tend to be the ones that divide the fanbase.
Author's Saving Throw: Penn's (and occasionally Teller's) use of profanity instead of straight out accusations of corruption and lies is meant to protect them against lawsuits. As weird as it may sound, it is safer to call someone a 'motherfucker' (which expresses an opinion, and thus is protected by Freedom of Speech) than a 'liar'. Though, since they gave away the "code" during the first episode, they still had to be a little careful. Seeing as how no one managed to successfully sue them over the show, it seems to have worked.
Broken Base: Although many of their "opponents" in the show are scammers, fanatics or just not very nice people, some of the audience does not accept the fact that the discussion nature of the show is purely formal, and most of the episodes represent a demonstrative derision and insult to supporters of the ideas that Penn and Teller criticize. This reached a special level after their episode about passive smoking, when they were forced to apologize after research that fully proved the harm of it.
The study they used as a reference for the second-hand smoke episode was a corporately funded exercise in Lies, Damned Lies, and Statistics, and had already been discredited when they made the episode.
In the "Taxes" episode, Penn tries to cite Al Capone's infamous 1932 conviction as evidence of how scary the American tax system really is, arguing that Capone was sent to Alcatraz for "tax evasion" because the government couldn't prove his more serious crimes—implying that the Feds can always use tax evasion as an "Ace in the Hole" if they really want to bust someone, but can't prove that they've done anything truly wrong. Except, if you know anything about Capone's trial, you'll know that tax evasion wasn't just a random crime that was unrelated to his criminal activities: he had vast sums of untaxed income because he ran a lucrative illegal bootlegging enterprise that he was trying to hide from the government, and his unpaid taxes were used as evidence of that.
Family-Unfriendly Aesop: Penn and Teller are often prone to opposing mainstream aesops in their show. Perhaps an especially memorable case is Holier Than Thou, wherein they had some memorably harsh criticisms of such popularly revered figures as Mother Teresa, Mahatma Gandhi and the Dalai Lama, but especially Mother Teresa.
Fridge Brilliance: At the end of the Season 4 intro, when Penn and Teller get hanged, Teller's feet are twitching. Teller is smaller than Penn, so of course it would take longer for him to hang. note This is even brought up in the Death Penalty episode. The point with hanging is having the victim's neck snap so they'll die instantly, but if you're too light, the neck might not snap so you'll suffocate instead.
"Funny Aneurysm" Moment: In the "Apocalypse 2012" episode, while discussing the idea that a brown dwarf star will destroy the world in 2012, they cut to Penn & Teller going up to Gary Coleman and asking if he's planning on destroying the world in 2012. He says yes. Coleman died unexpectedly in 2010.
Penn has told of his original pitch to the executives, which came 2 weeks after 9/11. As a part of it, he said that although he himself wasn't psychic, he could reasonably predict that within 6 months, psychic John Edward would announce a broadcast where he would channel the spirits of those who died in 9/11. It only took 3 months for Edward to do that, and the execs were impressed enough to greenlight the show.
One of the jokes in the PETA episode is about the logistical problems of 'freeing' all the domestic animals in the world and the point that if they have rights they have social responsibilities. Since the episode aired it came to light that PETA actually has a plan to deal with this: utter extermination of domesticated animals.
In that episode they already noted that PETA actually euthanizes most of the animals it rescues, making their stance for animal rights seem hypocritical. This extermination plan just adds to it. In fact, according to the state of Virginia, the percentage of animals euthanized by PETA the last few years has escalated over 90%.
The NASA episode blamed government cost-cutting for the Discovery and Challenger disasters, and implied that such things would be less likely under private corporations such as Virgin Galactic. Then came 2014...
Their episode on Vaccinations was incredibly important and brought to light some info that is much needed about vaccinations and autism. But as of February 2015 the Anti-Vaccination movement has seen a return and measles are coming back.
In the 2005 episode on government surveillance, they're impressed by the competence of a Kenyan immigrant compared to the other agents they study. "Yep! You gotta go to Kenya for a real American who can follow fucking directions!
A Running Gag in the animal activism episode was that you could accurately guess which side someone was on by their girth. In 2015 Penn really did lose more than a hundred pounds by switching to a (mostly) vegetarian diet.
That snail "mucas mask" gag from the first season became an actual fad about a decade later. Rendered down instead of applying the snails directly, but the justification is identical.
The shots of the baby receiving the operation in "Circumcision".
There's also the chiropractor operating on a little girl in Alternative Medicine. Penn even stops the film and sincerely warn us about the content beforehand.
The descriptions of botched executions in the Death Penalty episode. Pre-lethal injection anaesthetics not working properly, hanging where the victim's neck don't get snapped (both leading to strangulation) and the electric chair with the victim's flesh melting off, not much different from a certain execution in The Green Mile. Not to mention the medieval execution they mentioned on the side.
Retroactive Recognition: Since the show, being quasi-documentary in nature, went out of its way to find people in the public eye willing to talk about a particular subject the show was covering, it's likely you'll recognize someone who appeared on this show on other news or information programs (Jack Thompson from the "Video Games" episode, Richard Cohen from "Family Values", or Paul Watson from "Endangered Species" are particularly visible individuals, not to mention Sheriff Joe Arpaio). Given the show, you could call this trope, "Hey, it's that asshole!"
Tear Jerker: The episode "Mount Rushmore" ends with one. Throughout the episode one of Penn&Teller's people was soliciting signatures on petitions at the National Mall in Washington D.C. The petitions start out questionable, the first one is for a declaration of the supremacy of the United States to be brokered at the United Nations, but get progressively darker, with the last one essentially eliminating free speech. No matter how bad the proposal was, there were people who would sign the petition. At the end Penn notes that the people signing the petitions in the footage were the only people who actually signed; the vast majority of people refused to sign the petitions when they realized what they said.
Values Dissonance: Considering that P&T often deal with the extreme fringe of many ideological groups, this comes up a lot. For instance, the duo believes violence is only justifiable in defense of self or of innocent people (and they fall just short of total pacifism), so much horror and disgust ensues when interviewing someone who thinks violence is excusable to advance political causes, like environmentalism or animal rights.
What An Idiot: Some time after an episode debunking the use of chiropractors (not all forms, mind you; the main expert on their side was himself a chiropractor), a group of chiropractors bought tickets to their live show just to tell Penn and Teller that they were offended by the episode and are boycotting them.