It might be useful to have auto-generated tags for each API and add a link to the tag feed to the help page for that API. This would link directly the API documentation with the relevant discussions on SA, create a live FAQ.
For example, the autogenerated tag for the Comments API would be
Update: After browsing the currently existing tags, it looks like most of the APIs already have a tag created for them. However, I still think it'd be helpful if all the API-specific tags were visually different from the general tags (same way as the moderator-only or required tags are) and have a common prefix / are grouped together in the tags list.