Some informations about the text comparission used by LIKE: http://msdn.microsoft.com/en-us/library/bb221192 . The important thing for you:
You can use the special characters opening bracket ([ ), question mark (?), number sign (#), and asterisk (*) to match themselves directly only if enclosed in brackets.
What that means for you is that you need to replace # by [#]:
Code:
Me.Filter = "[Outage Investigation] Like '*" & Replace(Replace(Me.cmbOutageInvestigation, "[", "[[]"), "#", "[#]") & "*'"
You can add more replaces for * and ? but I commonly not escape them to make the filter form more powerful. The charlist "[" and the digit matcher # can get in handy as well, but be sure your users know how to use them properly. Perhaps with a reference to the link above from your filters form to allow them to look up the syntax.