The document could not be opened for editing. A Windows SharePoint Services compatible application could not be found to edit the document.

This is very common issue with office documents.(Excel , Word)
Most of the time issue has been resolved by hot fixes provided by Microsoft
This issue I found with MS Office Project documents and this works for me.
Please follow below steps to resolve MS Office Project document compatibility issue with SharePoint


1. On the local computer, install Windows SharePoint Services Support from the Office installation media.(It is listed under Office Tools.)


2. The following registry keys must be added to the local machine.


[HKEY_CLASSES_ROOT\MSProject.Project]
@="Microsoft Office Project Document"


[HKEY_CLASSES_ROOT\MSProject.Project\CLSID]
@="{74B78F3A-C8C8-11D1-BE11-00C04FB6FAF1}"


[HKEY_CLASSES_ROOT\MSProject.Project\CurVer]
@="MSProject.Project.9"


[HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\App
Paths\Winproj.exe]
@="\"C:\Program Files\Softricity\SoftGrid for Windows Desktops\sfttray.exe" /launch
"Microsoft Office Project 2003 projecpm.311""
"UseUrl"="1"
"SaveUrl"="1"
--note that "Microsoft Office Project 2003 projecpm.311" refers to the actual name
of the package. The name will be different for every case.


[HKEY_CLASSES_ROOT\.mpp]
@="MSProject.Project.9"
"Content Type"="application/vnd.ms-project"
"SoftGridSource"="{C5F5D9DD-0FE3-4421-A2BE-F8203F53EAD9}"