It seems i was too fast calling it off. I have now been able to reproduce the behavior on the test server.
The example can be found at
test.idempiere.org.
Log in as GardenAdmin and open the Two Tab Test window.
Here the search window will show the behavior I have described in my first post.
Note that the Parent Item column is a number and not a String (Foreign key restraint to the primary key column of the same table.)
The error appears when the stored Parents search preset is called up.

I had actually created the setup to illustrate another quirk and maybe the search window error has something to do with that.
I thought it would be a good idea to have the same table in a parent and a child tab in the same window.
This way I can display the child items (if present) in the child tab which IMO is actually a useful thing to have.
However this causes another interesting issue:
The key column of the table is accessed through a foreign key from another table column that uses a search reference.
What happens is that the columns are duplicated in the search dialog grid.
Menu > Item Search Test > Two Tab Test > Search Dialog
The Columns are displayed correctly when the child tab is removed from the Two Tab Test window.
I am afraid I have not been able to check wether this also heals the search window issue.
Best regards
Andreas