Invalid or Unqualified Reference Error

Range("A" & Rows.Count).End(xlUp).Row

I don't think you want periods on this line. I believe that is used with a 'With/End With' clause.

I believe that will include the ones below too. It might be quicker to add

with ws
'code
end with

Perhaps, with the missing With.

Sub Year_Fix()

Dim Rng1 As Range, Rng2 As Range, Rng3, Rng4 As Range
Dim LastRow As Long
Dim ws1 As Worksheet

    For Each ws1 In ActiveWorkbook.Worksheets

        With ws1
            With .Columns("K:K")
                .Insert Shift:=xlToRight, CopyOrigin:=xlFormatFromLeftOrAbove
                .Insert Shift:=xlToRight, CopyOrigin:=xlFormatFromLeftOrAbove
                .Insert Shift:=xlToRight, CopyOrigin:=xlFormatFromLeftOrAbove
            End With
            LastRow = .Range("A" & .Rows.Count).End(xlUp).Row

            Set Rng1 = .Range("N2", .Cells(LastRow, 14))    'Original
            Set Rng2 = .Range("M2", .Cells(LastRow, 13))    'Year
            Set Rng3 = .Range("L2", .Cells(LastRow, 12))    'Century
            Set Rng4 = .Range("K2", .Cells(LastRow, 11))    'Date

            Rng4.Formula = "=IF(N2>0,TEXT(N2,""dd/mm/""),"""")"
            Rng3.Formula = "=IF(N2>0,LEFT(TEXT(N2,""yyyy""),2),"""")"
            Rng2.Formula = "=IF(N2>0,RIGHT(TEXT(N2,""yyyy""),2),"""")"

            Rng4.Select
            Rng4.Copy
            Rng4.PasteSpecial Paste:=xlPasteValues

            Rng3.Copy
            Rng3.PasteSpecial Paste:=xlPasteValues

            Rng3.Replace What:="19", Replacement:="20", LookAt:=xlPart, _
                         SearchOrder:=xlByRows, MatchCase:=False, SearchFormat:=False, _
                         ReplaceFormat:=False

            Rng2.Copy
            Rng2.PasteSpecial Paste:=xlPasteValues

'            Rng1 = Rng3 & Rng2 & Rng4

            Rng1.Copy
            Rng1.PasteSpecial Paste:=xlPasteValues

            'Remove the helper columns
            .Columns("K:M").Delete Shift:=xlToLeft

        End With

    Next ws1

End Sub

By the way, I've commented out this line because it will error

            Rng1 = Rng3 & Rng2 & Rng4

if you are trying to do some sort of concatenation involving 3 ranges have a look at using a formula.