These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
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.
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.
"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.
Harsher in Hindsight: 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.
Hilarious in Hindsight: 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!
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.
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 or Richard Cohen from "Family Values" are particularly visible individuals, not to mention Sheriff Joe Arpaio). Given the show, you could call this trope, "Hey, it's that asshole!"
Strawman Has a Point: In the episode on old people, when discussing right-to-die issues, they say that, even though they're opposed to the physician who wants to keep physician-assisted suicide illegal, it's hard to call him an asshole when all he wants to do is not kill people.
What an Idiot: Some time after an episode debunking the use of chiropractors (not all forms, mind you), 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.