Excel VBA script really slow

I think the actual slowness of OP code is due to useless loops

here's a code with same results as OP's one but looping through cells only when necessary

Option Explicit

Sub SubMine()
Dim lastRowUsedPtLog As Long, lastRowUsedReport As Long
Dim lastRowUsedControlVisitNoDate As Long, lastRowUsedControlDateNoMatch As Long

Dim ptLogDdateVisit As Long
Dim reportPatientNr As Long, reportNrVisit As Long, reportDateVisit As Long

Dim reportSht As Worksheet, ptLogSht As Worksheet, controlSht As Worksheet

Dim ptLogPatientNrs As Range, ptLogPatientNrCells As Range, ptLogPatientNrCell As Range
Dim ptLogVisitNrs As Range, ptLogNrVisitCell As Range, ptLogDateVisitCell As Range
Dim reportPatientNrs As Range, reportPatientNrCell As Range
Dim ptLogCellsToMark As Range


Application.ScreenUpdating = False
Application.EnableEvents = False
Application.Calculation = xlCalculationManual

Set reportSht = Sheets("Report")
Set ptLogSht = Sheets("PtLog")
Set controlSht = Sheets("CONTROL")

' to avoid first "Union()" method call to fail, I set a dummy ptLogCellsToMark
With ptLogSht
    Set ptLogCellsToMark = .Cells(1, .Columns.Count)
End With

lastRowUsedPtLog = GetLastRow(ptLogSht, 5)
lastRowUsedReport = GetLastRow(reportSht, 2)
lastRowUsedControlVisitNoDate = GetLastRow(controlSht, 2)
lastRowUsedControlDateNoMatch = GetLastRow(controlSht, 9)

Set ptLogPatientNrs = ptLogSht.Cells(2, 5).Resize(lastRowUsedPtLog) 'list of PatientNr in "PtLog" sheet
Set ptLogVisitNrs = ptLogSht.Range("K1:T1") 'list of VisitNr in "PtLog" sheet
Set reportPatientNrs = reportSht.Cells(2, 2).Resize(lastRowUsedReport) 'list of PatientNr in "Report" sheet

For Each reportPatientNrCell In reportPatientNrs 'loop through PatientNr of "Report" Sheet

    reportPatientNr = reportPatientNrCell.Value ' track patientNr value from "Report" sheet
    Set ptLogPatientNrCells = FindValues(reportPatientNr, ptLogPatientNrs) ' find ALL occurencies of that patientNr value in "PtLog" sheet
    If Not ptLogPatientNrCells Is Nothing Then ' if there's an occurrence of that patientNr in "PtLog" sheet

        reportNrVisit = reportPatientNrCell.Offset(, 2) ' now it makes sense to track nrVisit value from "Report" sheet
        Set ptLogNrVisitCell = ptLogVisitNrs.Find(reportNrVisit) ' search for that nrVisit value in "PtLog" sheet
        If Not ptLogNrVisitCell Is Nothing Then ' if there's an occurrence of that nrVisit value in "PtLog" sheet

            reportDateVisit = reportPatientNrCell.Offset(, 4) ' now it makes sense to track dateVisit value from "Report" sheet

            For Each ptLogPatientNrCell In ptLogPatientNrCells 'loop through ALL occurencies of report patientNr of "PtLog" Sheet

                Set ptLogDateVisitCell = ptLogSht.Cells(ptLogPatientNrCell.Row, ptLogNrVisitCell.column) 'set the "PtLog" sheet cell with the date corresponding to patientNr and nrVisit from "report" sheet
                ptLogDdateVisit = ptLogDateVisitCell.Value

                Select Case True
                    Case ptLogDdateVisit > 0 And reportDateVisit = 0
                        lastRowUsedControlVisitNoDate = lastRowUsedControlVisitNoDate + 1
                        controlSht.Cells(lastRowUsedControlVisitNoDate, 2).Resize(, 3) = Array(reportPatientNr, reportNrVisit, ptLogDdateVisit) ' write in "CONTROL" sheet . NOTE: I added "ptLogDdateVisit" to keep track of what was date was not peresent in "Report" sheet

                    Case ptLogDdateVisit = 0 And reportDateVisit > 0
                        With ptLogDateVisitCell
                            .Value = reportDateVisit 'correct the "PtLog" sheet date value with the "Report" sheet one
                            Set ptLogCellsToMark = Union(ptLogCellsToMark, .Cells(1, 1)) ' add this cell to those that will be formatted at the end
                        End With

                    Case Else
                        lastRowUsedControlDateNoMatch = lastRowUsedControlDateNoMatch + 1
                        controlSht.Cells(lastRowUsedControlDateNoMatch, 9).Resize(, 4) = Array(reportPatientNr, reportNrVisit, reportDateVisit, ptLogDdateVisit) ' write in "CONTROL" sheet
                End Select

            Next ptLogPatientNrCell

        Else

            ' here code to handle what to do when a nrVist in "Report" sheet is not present in "PtLog" sheet

        End If


    Else

        ' here code to handle what to do when a patientNr in "Report" sheet is not present in "PtLog" sheet

    End If

Next reportPatientNrCell

With ptLogCellsToMark.Font
    .Color = -1003520
    .TintAndShade = 0
End With


Application.ScreenUpdating = True
Application.EnableEvents = True
Application.Calculation = xlCalculationAutomatic

End Sub


Function FindValues(valueToFind As Variant, rngToSearchIn As Range) As Range
Dim cell As Range, unionRng As Range
Dim firstAddress As String

With rngToSearchIn
    Set cell = .Find(What:=valueToFind, LookAt:=xlWhole)
    If Not cell Is Nothing Then
        firstAddress = cell.Address
        Set unionRng = cell
        Do
            Set unionRng = Union(unionRng, cell)

            Set cell = .FindNext(cell)
        Loop While Not cell Is Nothing And cell.Address <> firstAddress
        Set FindValues = unionRng
    End If
End With

End Function


Function GetLastRow(sht As Worksheet, column As Long) As Long
With sht
    GetLastRow = .Cells(.Rows.Count, column).End(xlUp).Row
End With
End Function