Attempting to apply a hotfix to my SCCM 2007 R3Primary server, I recieved an error 2147942487 (The parameter is incorrect). Googling this showed all kinds of non relevant pages!
My error: When the hotfix prompted me to specify a name for the client patch, I appended the purpose of the patch to the name.
The Issue: SCCM has a maximum allowable length for the package name which the Hotfix had allowed me to exceed.
The Solution: Keep the suggested name, then change it later on in the SCCM console.