Maybe this will help?

Hyperlink["https://mathematica.stackexchange.com/questions/9280/open-\ two-copies-of-the-same-notebook", \

CreatePalette[
  Button["Duplicate Active Notebook", 
   NotebookPut[
    NotebookGet[
      InputNotebook[]] /. {Rule[DockedCells, _] :> Sequence[], 
      Rule[WindowMargins, _] :> 
       Rule[WindowMargins, {{0, Automatic}, {0, Automatic}}], 
      Cell[x___] :> Cell[x, Evaluatable -> False]}, 
    Background -> GrayLevel[0.95], Editable -> False, 
    "ClosingSaveDialog" -> False, 
    DockedCells -> 
     With[{sourcenb = InputNotebook[]}, 
      Cell[BoxData[
        ToBoxes[Button["Update", 
          SelectionMove[InputNotebook[], All, Notebook];

          NotebookWrite[InputNotebook[], 
           NotebookGet[sourcenb] /. 
            Cell[x___] :> Cell[x, Evaluatable -> False]]]]], 
       "DockedCell", CellContext -> Cell]], 
    WindowTitle -> 
     "Duplicate of " <> 
      AbsoluteOptions[InputNotebook[], WindowTitle][[1, 2]]];
   SetSelectedNotebook[InputNotebook[]]], WindowTitle -> "Duplicate"];

Regards,...Jos

One alternative is to open a second instance of Mathematica by right-clicking on the icon in the task-bar and then clicking on the icon again. Then open the same notebook in both instances and but them side-by-side. But the problem here is that a modification in one instance will not be delegated to the other instance. So modifications should only be made in one instance otherwise parts will be lost. So it's also a "low-tech" solution.

That would be a very useful new feature in Mathematica. I often use a "low-tech" solution with my desktop and laptop computers open side-by-side.