Edit Document requires a Windows SharePoint Services-compatible application

Edit Document requires a Windows SharePoint Services-compatible application and Microsoft Internet Explorer 6.0 or greater

This error can be occurred from many reason, here are some of these:

You connect to a Microsoft Windows SharePoint Services website.

You view a document library.

You try to edit a Microsoft Office document that is stored in the document library.

I have resolved this issue and tested under multiple versions i.e. office 2003, office 2007, office 2010 and office 2013

For office 2003 and office 2007 [same resolution]:

1)   Click Start, and then click Control Panel.

2)   Click Add or Remove Programs.

3)   In the list of installed programs, click Microsoft Office 2003 or Microsoft Office 2007, and then click Change.

4)   Click Reinstall or Repair.

5)   Click OK.

For office 2010:

1)   Click Start

2)   Control Panel

3)   Programs

4)   Programs and Features

5)   Click the Office program you want to repair, and then click Change.

6)   In Office 2010

7)   Click Repair

8)   Continue.

For office 2013:

1)   Click Start

2)   Control Panel

3)   Programs

4)   Programs and Features

5)   Click the Office program you want to repair, and then click Change.

6)   In Office 2013

7)   click either Quick Repair or Online Repair