I recently patched my DMX 3.0 module and am experiencing the same problem (search failure).  I checked the version 3 'demo' module you have for DMX 3.0 (here at bring2mind) and found that the error is occurring here as well.   This was not an issue prior to performing the patch upgrade.  

As you suggested, I tested out the SQL Statement replacing {objectqualifier} with dbo and determined the problem to be at the following point highlighted in black:

An error occurred in the following search:
SELECT e.*, ext.Icon16, (SELECT Description FROM {objectQualifier}DMX_Entries AS p WHERE p.EntryId = {objectQualifier}DMX_Entries.CollectionId) AS CollectionName, 1 AS Rank FROM {objectQualifier}DMX_Entries e INNER JOIN {objectQualifier}DMX_Extensions ext ON e.EntryType = ext.ExtensionKey WHERE ((e.PortalId = 0) AND (ext.PortalId = 0) AND (e.EntryId = e.LastVersionId)) AND ((e.Description LIKE '%fha%'))

If you change the highlighted portion to "p.CollectionId" the statement will not error. 

Incidently, the error code you get in SQL Server is the following:

"Msg 4104, Level 16, State 1, Line 1

The multi-part identifier "dbo.DMX_Entries.CollectionId" could not be bound." 

This seems to point at the qualifier as being the culprit.