Anachronism

Anachronisms were objects, ideas or persons that were liable to create a time paradox. (AUDIO: The Carrionite Curse)

Regulation

The Time Lords's First Law of Time set out to prevent anachronisms such as a person meeting other versions of themselves (TV: The Three Doctors) or returning Eldrad to her present, by that time (from a 20th century point of view) the distant past. (TV: The Hand of Fear)

Serious instances

When anti-time began to bleed into the universe, anachronisms began to affect history and had a disastrous effect on the Web of Time. (AUDIO: Neverland)

Examples of their creation

The Monk had, by the time he met the First Doctor in 1066, caused many deliberate anachronisms in Earth history to "improve" it. (TV: The Time Meddler) The Fourth Doctor caused anachronisms of his own by deliberately defacing copies of the Mona Lisa, writing with felt tip pen on the canvas, "This is a fake". The words were readable in the 20th century after X-rays had been discovered. (TV: City of Death)

While in 18th century France, the Tenth Doctor thought he may have "invented the banana daiquiri a few centuries early". (TV: The Girl in the Fireplace)

The First Rani created anachronisms in the alternate Rome on Terra Nova. (PROSE: State of Change)

Upon seeing a Sontaran teleport pod in the Rattigan Academy, the Tenth Doctor told Luke Rattigan that "it might be Earth technology, but that's like finding a mobile phone in the Middle Ages", pointing out that the presence of such futuristic technology was an anachronism. (TV: The Sontaran Stratagem)

Spending three weeks in 1138 Essex, the Twelfth Doctor entered an axe battle playing an electric guitar solo while riding a tank, and introduced its citizens to the word "Dude" several centuries too early. Missy had ironically told Clara Oswald to keep her eyes open for the slightest anachronisms prior to the Doctor's entrance. When Colony Sarff arrived, he threw a heavily weather-beaten sonic screwdriver at the Doctor's feet; after he, Clara, and Missy were taken to be brought to Skaro, the screwdriver, tank, and guitar were all left behind. (TV: The Magician's Apprentice)

WillH noted that there weren't many people in the 19th century who wore leather jackets after he found photographs of the Ninth Doctor in a book of photos of Victoria. (PROSE: Have You Seen This Man?)

Examples of their prevention

The First Doctor warned Barbara Wright against attempting to change 15th century Aztec culture. (TV: The Aztecs)

Both Rose Tyler (TV: The Unquiet Dead, PROSE: The Clockwise Man) and Jack Harkness (TV: The Empty Child) made it a point to dress appropriately for the time period they were in; much to their ire, the Ninth Doctor opted to change his shirt rather than his conspicuous leather jacket. (TV: The Unquiet Dead)

Since portable stereos did not exist in the 1960s, the Seventh Doctor called the tape deck that Ace carried around with her in Shoreditch in November 1963 a "dangerous anachronism". (TV: Remembrance of the Daleks)

The Doctor had refused to give a mobile phone to Sarah Jane Smith on the basis that it was "anachronistic". She later remarked that, despite this attitude, he'd gifted her K9. (COMIC: Vortex Butterflies)