According to Wikipedia, continuity is "consistency of the characteristics of persons, plot, objects, places and events seen by the reader or viewer" of fictional works.
The term may be applied in the Grand Theft Auto series to compare the consistency in a number of fictional topics in each game. It is difficult to ascertain whether continuity errors in many of the games are intentional or not, as settings and characters have been frequently redesigned, while plot lines in certain games are known not to relate to each other. It can be assumed Rockstar North, the series' primary developer, has little regards to continuity when the need arises.
A degree of effort was made to maintain continuity between GTA III and GTA Vice City Stories, with many characters recurring between titles, the settings maintaining their designs, and GTA III's plot expanded. Minor continuity errors, however, were still persistent in this part of the series. Similarly, continuity in GTA IV (including its episode packs) and GTA Chinatown Wars remain, although they no longer appear to be linked to previous games.
One of the most glaring lack of continuity is the design of cities in the series. The three cities of Grand Theft Auto 1, Liberty City, San Andreas and Vice City, would go on to be featured in future games, but were significantly redesigned, with San Andreas redone as a state with three cities. Liberty City, in particular, has the highest total of three iterations, barring another two adapted for handheld console versions, as of 2009. Other locales, such as London and Anywhere City, were not featured again after their first appearances.
For games between GTA III and GTA Vice City Stories, their settings maintained a degree of consistency in layout and appearance when featured again in another game, although all of them would be set years before GTA III and thus would also receive changes in certain locations of the settings. GTA San Andreas would even feature a segment of Liberty City as featured in GTA III, confirming the city's existence with San Andreas. All in all, the games' iteration of Liberty City has been featured three times (four if GTA San Andreas is counted), followed by Vice City with two appearances, and San Andreas with only one appearance.
For much of the series, many characters in the series were largely disposable, appearing only once in a game. This was most apparent in GTA 1, GTA London 1969, GTA London 1961 and GTA 2, where the many bosses the player works will never appear again in succeeding games (as they would be dead). However, certain elements of past characters have been reused, as is the case with El Burro and Claude Speed.
The only line of games to extensively reuse characters are games between GTA III and GTA Vice City Stories, where characters introduced in a game would reappear in an older or younger form in games released after. Despite the attempted continuity in the games, several minor continuity errors may be noted, such as their appearance, mannerism and personality.
GTA IV started anew by dropping all characters featured in previous games, justifying all of them would be dead regardless, while establishing a new cast of characters intended to appear in the same timeline in the base game, The Lost and Damned, The Ballad of Gay Tony and GTA Chinatown Wars. Exceptions to the case are recurring personalities of past radio stations. Lazlow, who has extensively appeared on radio in various games between GTA III and GTA Vice City Stories, is present in Integrity 2.0, the game alluding to Chatterbox FM, which Lazlow hosted in GTA III and GTA Liberty City Stories. Likewise, Fernando Martinez cameos in The Ballad of Gay Tony in the form of a radio DJ for Vice City FM.
In early games, plot lines were not made to interconnect each other. As characters and settings differ between the games, it is assumed the games each feature their own distinct storyline and thus were not related. Between GTA III and GTA Vice City Stories, however, the original plot of GTA III was expanded towards the past, providing backgrounds on various events and characters. GTA IV and games later, however, do not reference events in previous games, setting themselves apart from their predecessors, except for certain easter eggs, like graffiti inside apartment buildings saying that every protagonist from the GTA III Era had died or been killed, and Lazlow mentioning working on radio stations in the GTA III Era.