There is no way to reference a specific quote on Wikiquote. If I want to direct a person or a machine to a specific quote, that is impossible. This severely limits the utility of Wikiquote, since a user/machine will always have to copy the text from Wikiquote instead of referencing a specific quote.
On the page for [[ https://en.wikiquote.org/wiki/Abraham_Lincoln | Abraham Lincoln ]], if you want to reference the quote
> I am a slow walker, but I never walk back.
The closest you can get is the section [[ https://en.wikiquote.org/wiki/Abraham_Lincoln#1860s | 1860s ]].
Since this is a list of unrelated quotes (that just happened to be in that decade), there's no way to direct a user (or machine) to that specific quote without copying the text (as I did above). This means there's not really a point in referencing Wikiquote as I had to copy the text anyways.
Add [[ https://en.wikipedia.org/wiki/Permalink | permalinks ]] to quotes. Since the quote text might change (be improved, etc.) it might be best to give quotes ids (of some kind) so they can be updated or destroyed, but their id will not change.
* Create a template that each quote should be wrapped with that would give a fixed id for each quote.
* Use [[ https://www.mediawiki.org/wiki/Extension:Wikibase_Repository | Wikibase Repository ]], [[ https://www.semantic-mediawiki.org/wiki/Semantic_MediaWiki | Semantic MediaWiki ]], or [[ https://www.mediawiki.org/wiki/Extension:Cargo | Cargo ]] to store/retrieve quotes from the wiki page.
* Create a custom extension for saving each quote as it's own namespace, but updates the UI to expose this similar to the way it is now.
* Use something other than MediaWiki for Wikiquote.