I build a simple API for a bookmark manager, where the URL of record should only be stored once. Record 001 with www.example.com already exists beside record 002 with www.stuff.com.
If I update record 002 with the url www.example.com, should I ignore the complete request and send back an error message or is it better to update all valid parts and just send an errror message, that says, that the url/bookmark already exists?
With a PUT, the expectation is that the entire operation will succeed or fail:
The PUT method requests that the state of the target resource be created or replaced with the state defined by the representation enclosed in the request message payload. A successful PUT of a given representation would suggest that a subsequent GET on that same target resource will result in an equivalent representation being sent in a 200 (OK) response.
https://www.rfc-editor.org/rfc/rfc7231#section-4.3.4
You should send an error for an invalid PUT (since the URL already exists and cannot be in two records at the same time) and not apply any of the other updates.
For partial updates you might consider a PATCH, but in this case I don't think you would go this direction since:
If the entire patch document cannot be successfully applied, then the server MUST NOT apply any of the changes.