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.
Accidental Innuendo: Sometimes seen in Colemanballs / Commentatorballs, and they also occasionally publish examples of this from newspaper articles (this used to be a much more prevalent feature, back when manual typesetting meant that amusing typos were more common in newspapers).
Broken Base: Their treatment of Julian Assange is unrelentingly negative - as far as the Eye is concerned, he is a shifty, anti-Semitic, irresponsible, vain sex offender. This has fractured the base into people who agree with this treatment and people who think that the Eye and Assange are natural allies.
A joke in the issue released after Bloody Sunday (where thirteen Irish marchers were shot dead by panicked British paratroopers) featured Lord Carrington talking to Reginald Maudling, saying "Six and a half brace [of game birds], eh?" "Not bad for this time of year!" The people of Derry didn't see the funny side.
The front page◊ after Diana died was banned in several shops and is still the most-sought after issue.
Every other issue usually carries some form of letter from an outraged reader who "never normally complains" but last week's cartoon "went too far."
The mocking of Sarah and Gordon Brown when they talked about their son dying on TV. The Eye's line, that they two were exploiting a personal tragedy for political capital, was criticized in some quarters.
The magazine ran a spoof article after the death of Michael Jackson entitled "Mad Pedophile Dead."
The magazine was also kicked for a cartoon after a fatal bobsleigh accident showing a coffin going down a bobsleigh track.
American readers were less than amused by a cartoon of Barack Obama talking to a general (modeled on William G. Boykin) with the title "New Surge in Afghanistan?" With Obama asking "Should we send more troops to Arlington?" Arguably, however, the magazine didn't intend this to be funny.
They got quite a bit of this when they commemorated the death of Margaret Thatcher with a special edition, featuring a play on a famous anti-Thatcher slogan as its cover joke.
Memetic Mutation: The Eye's nicknames for newspapers are regularly used by people who have never read and have barely heard of Private Eye. For a more narrow, political audience, their euphemisms such as "tired and emotional" and "discussing Uganda" are well known.
The Weird Al Effect: Some phrases the Eye has kept going are now more associated with it than their original progenitors, such as "as any fule kno", which comes from molesworth.