Loose Continuity

Loose Continuity refers to an overall canon to a story or franchise that have some rather contradictory elements included in their run. For example an event that might cause a character's relationship in one showing does not show up in following events, or revelations that were not mentioned before appear instantly. This is commonly seen in comedy or episodic series (e.g. Lupin III) or franchises that are given complete creative freedom including the works by Leiji Matsumoto.

Examples in the Leijiverse
Leiji Matsumoto outright stated that he dislikes the notion of continuity, as such depictions of events are shown in different ways with no timeline said to be concrete. Below are the most common examples:

Tochiro's Death
In series that show the death of Tochiro Oyama, Tochiro has either died in battle, succumbed to illness, or died in a number of accidents.

Arcadia's Creation and Design
While most of the time, the Arcadia was created by Tochiro, contracting a disease forces Tochiro to get help from Tetsuro Hoshino to upload his consciousness into the Arcadia. Other times, Tochiro did it himself with only Bird at his side. The Arcadia also has a few different designs by series, including a blue or green coloration (in real time this was due to marketing issues).

Tadashi Daiba
Tadashi Daiba in most of his appearances in a new series is a new recruit on the Arcadia, including series that are supposed to be sequels including Endless Odyssey.

Emeraldas and Maetel
When originally appearing together, Emeraldas and Maetel are implied to be good friends or have not met each other before. In later series, especially the Maetel Legend OVAs, they are sisters.

Captain Harlock and Emeraldas
Harlock and Emeraldas are stated to have met each other on different occasions, including long before either of them met Tochiro while others have Emeraldas as a newcomer.

Emeraldas
In some of her early animated appearances, Emeraldas lacks her facial scar, in the Captain Harlock anime she is even called Emeralda.

Cosmo Dragoon
The Cosmo Dragoon guns were originally stated to have four produced but later series included a fifth. Which person owning the exact model is also different per series.

Mayu
Mayu only makes seldom appearances throughout some series, other times she does not appear at all as her father Tochiro was said to have died before conceiving her with Emeraldas.