Discontinuity refers to the concept of striking a given aspect of a continuum from one's own personal interpretation of the canon. The term appears to have been popularized by TV Tropes, but the concept has existed since well before then.
Given the wide variety of tastes people have, it's only natural that there will be certain aspects of a work of fiction certain people dislike. This especially true of large universes that span multiple authors, such as Star Wars and the Marvel Universe. Discontinuity occurs when fans elect to ignore the elements of canon that they do not care for. Those with a particular vitriol for said elements may choose to go on the offensive, declaring that certain events never occurred and that the official canon is thus incorrect.
There are some cases where elements of a canon are ignored, reversed, or done away with by the creator(s) of the canon (see Retcon). This can be done for a variety of reasons, including bowing to fan outcry or personally not liking the material. Some notable cases of canon discontinuity are:
- The third and fourth Superman films
- Fallout: Brotherhood of Steel, along with much of Fallout Tactics, the sillier aspects of Fallout 2, and the original ending of Fallout 3
- The 1980 reboot of Battlestar Galactica
- Almost all of the pre-series Buffy the Vampire Slayer film
Though various PPC agents may have pet peeves about their fandoms, it is a rare agent who outright endorses discontinuity, as the concept, in its more extreme forms, can cause great harm to the continua. The most prevalent problem caused by discontinuity is the "fixfic," a type of fanfic that attempts to "correct" perceived "problems" with the continuum. Aside from that, discontinuity is probably third only to ships and subbing vs. dubbing as a cause for fandom-based flamewars.
On a personal note, practicing discontinuity is unlikely to get you much sympathy from Agent Samuel, among many others.