Sorry for the vague summary, I'm not sure where to start with this and it might be multiple tickets...

http://beta.musicbrainz.org/ws/2/work/a1bcf2c1-ef31-4aa8-b01c-97e0fc9ef361?fmt=json&inc=artist-credits says:
error: "artist-credits is not a valid option for the inc parameter for the work resource unless you specify one of the following other inc parameters: releases, release-groups, recordings, works"

but if you try any of those:

http://beta.musicbrainz.org/ws/2/work/a1bcf2c1-ef31-4aa8-b01c-97e0fc9ef361?fmt=json&inc=artist-credits+releases says:
error: "releases is not a valid inc parameter for the work resource."

http://beta.musicbrainz.org/ws/2/work/a1bcf2c1-ef31-4aa8-b01c-97e0fc9ef361?fmt=json&inc=artist-credits+release-groups says:
error: "release-groups is not a valid inc parameter for the work resource."

http://beta.musicbrainz.org/ws/2/work/a1bcf2c1-ef31-4aa8-b01c-97e0fc9ef361?fmt=json&inc=artist-credits+recordings says:
error: "recordings is not a valid inc parameter for the work resource."

http://beta.musicbrainz.org/ws/2/work/a1bcf2c1-ef31-4aa8-b01c-97e0fc9ef361?fmt=json&inc=artist-credits+works says:
error: "works is not a valid inc parameter for the work resource.

i.e. none of the inc parameters it says to use actually work, which means the error message is wrong.

In other cases, inc=artist-credits causes artist credits to be included for relevant entities linked via relationships. e.g. https://musicbrainz.org/ws/2/release-group/315f9309-b69c-4c48-83df-273e2d7a4422?inc=release-group-rels+artist-credits includes the artist credit for the linked release group too.

That would suggest that the original URL shouldn't actually cause an error and that artist-credits should cause artist credits to be included for the linked recordings.

Similarly, http://beta.musicbrainz.org/ws/2/artist/1283f619-2789-4892-af46-29a13e5cca5b?inc=recording-rels+works includes recording relationships without the artist credits.
and http://beta.musicbrainz.org/ws/2/artist/1283f619-2789-4892-af46-29a13e5cca5b?inc=recording-rels+works+artist-credits includes recording relationships with artist credits.

But if I do http://beta.musicbrainz.org/ws/2/artist/1283f619-2789-4892-af46-29a13e5cca5b?inc=recording-rels+artist-credits it says error: "artist-credits is not a valid option for the inc parameter for the artist resource unless you specify one of the following other inc parameters: releases, release-groups, recordings, works".

From the behaviour, it seems that artist-credits should actually be valid for release-group-rels, release-rels and recording-rels for all entities.