Internally, SharePoint server uses "_layouts/filter.aspx" application page for filter values which are presented in an iFrame. I checked the ULS logs and copied the Request URL with filter.aspx. I pasted it in browser and hit "Enter". It returned no result.
What is multi-valued field?
The field which allows more than one values or which allows multiple selections. The multi-valued fileds are non-sortable, non-filterable. Multi-valued fields cannot be indexed.
This behavior can be overridden. Every field has an associated schema. Multi-valued fields are marked as "Sortable =false" in the schema for performance reasons. Note: Apply the workaround wherever it is unavoidable.
If we mark the multi-valued PeoplePicker as "Sortable=true", the column turns filterable/ sortable. This can be achieved using SharePoint Server Object Model or using Windows PowerShell (I love it).
PowerShell Script to mark the column as Sortable:
$web=Get-SPWeb <weburl>$list=$web.Lists[<list title>]
$field.SchemaXml = $strSchema
[Update: I noticed that multi-valued "person or group" coulmn in other web application was showing filter choices even though "Sortable=false". Googling did not help. I checked at various levels and found that "Online Presence" setting causes this error. If Online presence setting is turned OFF, SP 2010 starts showing this error for multi-valued columns when tried to filter. So turn it ON, and...no error, filter choices are shown back. The Online Presence setting is available in Web applications's General Settings.]