The problem was non-contigent areas in the filter result.

Give this a try.
Private Sub CommandButton1_Click()
Dim Rng As Range
Dim are As Range
Dim lngCount As Long

    With Worksheets("Sheet1").ListObjects("Table1")

        With .Range
            .AutoFilter
            .AutoFilter 2, Sheet1.Range("F2")
        End With

        On Error Resume Next
        Set Rng = .DataBodyRange.SpecialCells(xlCellTypeVisible)
        On Error GoTo 0

        If Not Rng Is Nothing Then
            For Each are In Rng.Areas
                lngCount = lngCount + are.Rows.Count

            Next are
            Sheet1.Range("H2") = lngCount
            Sheet1.Range("H5") = Rng.Row
        Else
            Sheet1.Range("H2") = "none"
            Sheet1.Range("H5") = "No Row"
        End If
    End With

End Sub
PS Don't add On Error Resume Next anywhere else, if you encounter any other errors/problems post back.