If OutIY.Cells(i, "D") <> OutIY.Cells(i, "F") And WorksheetFunction.Int(Cells(i, "G").Value = WorksheetFunction.Int(today).Value) Then Cells(findit.Row, "G") = (Format(Now, "mm/dd/yyyy"))

....WorksheetFunction.Int(Date).Value ....

Option Explicit
Sub Test()
    Dim OutIY As Worksheet
    Dim AnotherSht As Worksheet
    Dim findit As Range
    Dim i As Long

    'change as needed
    Set OutIY = Worksheets("Output")
    Set WhichSht = Worksheets("Which Sheet should this be")
    Set findit = AnotherSht.Range("a1")

    ''was originally...
    'If OutIY.Cells(i, "D") <> OutIY.Cells(i, "F") And WorksheetFunction.Int(Cells(i, "G").Value = WorksheetFunction.Int(today).Value) Then Cells(findit.Row, "G") = (Format(Now, "mm/dd/yyyy"))
    'try...
    If (OutIY.Cells(i, "D").Value2 <> OutIY.Cells(i, "F").Value2) And (WhichSht.Cells(i, "G").Value2 = CLng(Date)) Then
        With WhichSht.Cells(findit.Row, "G")
            .Value2 = CLng(Date)
            .NumberFormat = "mm/dd/yyyy"
        End With
    Else
    'do nothing
    End If
        'release variables
        Set OutIY = Nothing
        Set AnotherSht = Nothing
        Set findit = Nothing
    End Sub

Sub Test()
    Dim OutIY As Worksheet
    Dim AnotherSht As Worksheet
    Dim findit As Range
    Dim i As Long

    'change as needed
    For i = 10 To Cells(Rows.Count, 1).End(xlUp).Row
    Set OutIY = Worksheets("Sheet1")
    Set WhichSht = Worksheets("Sheet1") ' ("Which Sheet should this be")
    Set findit = OutIY.Range("A:A").Find(what:=Cells(i, 1).Value)
     
    ''was originally...
    'If OutIY.Cells(i, "D") <> OutIY.Cells(i, "F") And WorksheetFunction.Int(Cells(i, "G").Value = WorksheetFunction.Int(today).Value) Then Cells(findit.Row, "G") = (Format(Now, "mm/dd/yyyy"))
    'try...
    If ((Cells(i, "D") <> Cells(i, "F")) And (WhichSht.Cells(i, "G").Value2 < CLng(Date))) Then
        With WhichSht.Cells(findit.Row, "G")
        Cells(findit.Row, "G") = Date
        Cells(i, "F") = Cells(i, "D")
          .Value2 = CLng(Date)
            .NumberFormat = "mm/dd/yyyy"
        End With
    Else
    'do nothing
    End If
        'release variables
        Set OutIY = Nothing
        Set AnotherSht = Nothing
        Set findit = Nothing
        Next i
        MsgBox "done"
    End Sub

Option Explicit

Sub Test2WithLotsOfComments()
    Dim OutIY As Worksheet
    'if using a set template file the number of header rows should not be changed within the _
     code, therefore by defining this as a Const (ie Constant) it can not be changed during the macro by mistake.
    Const FirstDataRow As Long = 10
    Dim i As Long
    Dim LastDataRow As Long

    'to speed up the macro (you could also turn off calculations & other actions/events but I don't _
     think it's needed in this situation).
    Application.ScreenUpdating = False

    Set OutIY = ThisWorkbook.Worksheets("Sheet1")
    'can remove the "WhichSht" because this is Set to be the same as the OutIY sheet therefore it is unnecessary.

    'by preceding all the "Cells(..." with a dot ie ".Cells(...", they become sub-ordinate to the _
     OutIY sheet Object in the below With Statement.
    With OutIY

        'remove this from the loop so that it is only calculated once (& there is no chance of it being changed within in the _
         loop, eg if a row was deleted).
        LastDataRow = .Cells(.Rows.Count, 1).End(xlUp).Row

        For i = FirstDataRow To LastDataRow

            'I think the below findit variable can be removed & replaced by the simpler use of the looping "i" variable (with _
             this belief, I've changed the remaining code to replace "findit" with "i").
            '### Using "i" assumes that a type of inventory will only appear once in the list, if this assumption is _
             inaccurate then you will need to use "findit", but NOTE, you may need to incorporate a loop to ensure that _
             all rows for the specific inventory type are checked & correctly adjusted.
            'delete this line...        Set findit = .Range("A:A").Find(what:=.Cells(i, 1).Value)

            'the code previously posted relied on the default property of the Cells property being Value, but _
             potentially this could change in a future version of Excel (unlikely but possible) therefore I _
             think it's better to always explicitly state the desired property as ".value" (see _
             brief comments @ http://www.dailydoseofexcel.com/archives/2004/07/07/the-strange-object/).
            'Also, I've used ".value2" for the date column due to potential Excel-VBA translation _
             problems demonstrated in http://support.microsoft.com/kb/182812
            If ((.Cells(i, "D").Value <> .Cells(i, "F").Value) And (.Cells(i, "G").Value2 < CLng(Date))) Then

                'move any code that doesn't need to be in the With statement outside it.
                .Cells(i, "F").Value = Cells(i, "D").Value
                'I've changed the following for speed ("in theory" but probably not actually noticeable) by moving the _
                 formatting outside the loop. therefore the below commented lines can be replaced by the _
                 subsequent uncommented line & the later formatting line identified with "'***"
                'With .Cells(i, "G")
                '    .Value2 = CLng(Date)
                '    .NumberFormat = "mm/dd/yyyy"
                'End With
            Else
                'do nothing
            End If
        Next i
        '*** added to format all dates in one go (after the loop has finished).
        .Range(.Cells(FirstDataRow, "G"), .Cells(LastDataRow, "G")).NumberFormat = "mm/dd/yyyy"
    End With

    'release variables.
    Set OutIY = Nothing
    'reset Excel settings
    Application.ScreenUpdating = True
    MsgBox "done"
End Sub