If I built my app against D3DX June2007_d3dx9_34 and the target system has a newer version Nov2007_d3dx9_36 should that be a problem?
I distribute D3DX DLLs using MS' redist-installer tool but I noticed one one 'clean' PC (no D3DX previously installed) I got an error about missing D3DX DLL. Before trying to figure out if the installer itself is not working, I wondered if maybe supplying a too-new version of the DLL is the problem - will the app be looking for a DLL with the exact name?
D3DX libraries are not backwards-compatible, and the API may change between versions. So the target system must have the same version of D3DX that you build your application with - a newer version won't work.
If you use Dependency Walker on your application, it should show you that there's a dependency on a DLL with the exact version number.