I haven’t updated my VM to latest updates for a long time and I decided to do that today. After Rollup was installed, I saw message that said Rollup was not applied to one or several organizations. I ignored that message and tried to log into CRM. I got following error:

So the Update Rollup was applied to all organizations except one. I found that it is possible manually to apply the update as shown on following screenshot (When you click on the organization record, additional options became available on a right panel):

I tried to update this organization manually, but I got the following screen as a result (not very informative actually):

I looked into log file and found the following explanation of an error:
System.Exception: Action Microsoft.Crm.Tools.Admin.InstallDatabaseUpdatesAction failed. —>
System.Reflection.TargetInvocationException: Exception has been thrown by the target of an invocation. —>
System.Data.SqlClient.SqlException: Column names in each table must be unique. Column name ‘IsMapiPrivate‘ in table ‘ActivityPointerBase‘ is specified more than once.
I’m appreciated to to my fellow MVP Ronald Lemmen, who came quickly to my aid with a solution. The solution was obvious but 100% unsupported:
1. Connect to the SQL Server in your CRM using SQL Server Management Studio.
2. Open the ActivityPointerBase table of organization you’re having problems with and delete IsMapiPrivate and LeftVoiceMail fields:

3. Re-run the Update of organization DB. This time the update was applied without any issues.