Converting PDF to any other format is one of the most complex things you can do with a PDF file. Unfortunately this is a case of "garbage in - garbage out" - the quality of your resulting file depends highly on the quality of the PDF file. This does not necessarily mean that the PDF file looks bad when displayed or printed, it is about the "inner quality" of the file. The problem is that low quality PDF generators will omit data that is required to convert back from a "glyph" (that is the drawing of a character) to the corresponding character.
In some cases, you will get better results when you save your PDF file as a set of TIFF images (File>Save As Other>Image>TIFF), then import these TIFF images back into Acrobat and OCR them before trying to export to Word again. This of course requires that you are using Acrobat and not the online ExportPDF service.