I know what it is. Some of the 31st Jan dates have time beyond 00:00:00 so comparing against Date(2012,1,31) doesn't include them.

Use

=COUNTIFS('Call Summary'!$C:$C,$A2,'Call Summary'!$H:$H,"inbound",'Call Summary'!$G:$G,"<="&DATE(2012,1,31)+TIME(23,59,59),'Call Summary'!$G:$G,">="&DATE(2012,1,1))