So I repaired the installation of DMO, restarted the Agent on the server, and no, the error came back. Removed DMO, reinstalled it and after a restart, the error came back.
Hmm. Strange. Looks like some components don’t land properly. So time for some searching. Since DMO is part of backward compatibility components, I looked for DMO related files in the folder: C:\Program Files\Microsoft SQL Server\80. Here two other folders are to be found as well: Tools and COM. Opened the Tools folder to find the folder Binn. There I found a dll with a nice name: SQLDMO.DLL.
Could it be that somehow this dll didn’t get registered? So I opened an elevated cmd-prompt, gave a cd-cmd in order to get to the right folder (cd C:\Program Files\Microsoft SQL Server\80\Tools\Binn), and gave this command: regsvr32 SQLDMO.DLL.
Restarted the Agent on the server, and now no more events with EventID 4000 appeared. After 10 minutes or so this SQL server appeared in OpsMgr and is being monitored now completely.
So whenever EventID 4000 keeps coming back on a SQL 2008 server, even when DMO has been installed as described in the SQL MP guide, there might be an issue with the dll (SQLDMO.dll) not being registered. Do it manually and then all is OK.