I still haven't got to the bottom of this and would appreciate any help. 

After querying the SearchItemWordPosition and related tables, what I do know is that the duplicate entries are not limited to a single DNN module, but include the list below. This must be an ongoing problem for others as well.

Announcements
DnnForge - NewsArticles
Documents
FAQs
Links
Media
Text/HTML
Wiki

The query I used to discover this is:

select distinct FriendlyName 
from ModuleDefinitions md
inner join Modules m
on md.ModuleDefId = m.ModuleDefId
where m.ModuleID IN (
select DISTINCT ModuleID
from SearchItemWordPosition siwp
inner join SearchItemWord siw
on siwp.SearchItemWordID = siw.SearchItemWordID
inner join SearchItem si
on siw.SearchItemID = si.SearchItemID
group by ModuleID, siw.SearchItemWordID, ContentPosition
having count(1) > 1)

Have added a comment in Gemini to the effect that this bug is still active in DNN701.

Thanks for the fix suggestion. Do you know if that approach has been tested? Sounds like it might cause errors in the indexing stored procedures.