I'm having the same problem, but think I have fixed it. I think there are two problems. The first is where mpiexec is installed. The default location is
c:\Program Files\Microsoft HPC Pack 2012\bin
There are spaces in the path. What I had to do was uninstall it, download the installer from the link in the TauDEM site (http://hydrology.usu.edu/taudem/taudem5/downloads.html), then reinstall it again, but this time specifying a path without spaces. Then I had to manually modify the System Path so that it would have the correct path to the mpiexec.exe.
The second issue is that when you save your output file, save it to a location without spaces in the path. Just creating a temporary output file doesn't seem to work, even though the path doesn't have spaces. I think that is because the default location is in the users appdata directory, it is probably a permissions issue.
Hopefully this helps.
Update, after playing with QGIS2.8 a little longer, I found that it wasn't necessary to reinstall the HPC to another directory. If I left it at the original location and simply set the MPICH2/Open MPI bin directory to c:\Program Files\Microsoft HPC Pack 2012/bin/ and the TauDEM command line tools folder to c:\Program Files/TauDEM/TauDEM5exe/ folders, it appeared to work.