Ah, I see now. Try this, hope it works for you:
Sub DateFormatChecking(columnname As Long)
Dim rowcount As Long
Dim R As Long, strVal
Dim String1 As String
Dim String2 As String
rowcount = Range("A65536").End(xlUp).Row
For R = 2 To rowcount
strVal = Sheet1.Cells(R, columnname).NumberFormat
String1 = Sheet1.Cells(R, columnname).Value
String2 = Sheet1.Cells(R, columnname).Value2
If String1 <> String2 Then
If strVal <> "mm/dd/yyyy" And strVal <> "mm/dd/yy" Then
Sheet1.Cells(R, columnname).Interior.ColorIndex = 3
Else
Sheet1.Cells(R, columnname).Interior.ColorIndex = 0
End If
Else
Sheet1.Cells(R, columnname).Interior.ColorIndex = 3
End If
Next
End Sub