Report Wizard: Query execution failed for data set 'DSMain'

There is a problem with the CRM 4.0 Report Wizard that can result in an error like the following:
An error has occurred during report processing.Query execution failed for data set 'DSMain'.The column 'accountid' was specified multiple times for 'account0'. The column 'accountid' was specified multiple times for 'opportunity1'.

Explanation of the problem
The ultimate cause is how the Report Wizard stores the Filtering Criteria for reports based on the account entity. The Report Wizard stores the query for any criteria as a combination of all fields in the account entity, and all fields in the related primary contact. When the report is run, the SQL query attempts to use the results of the following (or similar) as a table alias:

select DISTINCT account0.*, accountprimarycontactidcontactcontactid.* from FilteredAccount as account0 left outer join FilteredContact as accountprimarycontactidcontactcontactid on (account0.primarycontactid = accountprimarycontactidcontactcontactid.contactid) where (account0.statecode = 0)

This returns two fields called accountid (one from the account entity, and one from the contact), which breaks the main SQL query for the report, and gives the error above.

Resolution
The way to resolve this is to ensure that, when you create the report with the Report Wizard, you do not specify any criteria for the account entity. This will cause the Report Wizard to store the query as solely against the account entity. Once you’ve created the report, you can happily edit the default filter to whatever you want, and the report will work fine – the key factor is not having any criteria when you first create the report.

Unfortunately there’s not an easy way to fix existing reports with this problem – it should be possible to edit the data in the DefaultFilter column in the reportbase table, but this is unsupported. I’d suggest in this scenario that you’re best off recreating the report from scratch