SQL-DMO Install Required: This operation requires the SQL Server ODBC Driver, version 3.80 or later, which comes with SQL Server 2000, SQL Server 2005 and SQL Server Express.
This is caused by a missing dependency - SQL-DMO has been deprecated and is no longer part of the Sql Server. When you search the Web looking for solution you will be advised to install the "Backward Compatibility Components" which are part of the "Feature Pack for Microsoft SQL Server 2005". So I did. However, this caused another error:
An Application has made an attempt to load the C runtime library incorrectly.
Please contact the application's support Sql server team for more information.
Investigating this took me some time. It came out that when you search for "Feature Pack for Microsoft SQL Server 2005" in the Microsoft Download Center the first result you get is actually outdated. There is another download link at the bottom of the search results list, that points to the latest version:
Correct version: Feature Pack for Microsoft SQL Server 2005 SP4.
Installing this one fixed all issues and allowed me to run the OMPM. I had a 64x version of Sql Server 2008 R2.