Re: L.A. Noire Saveset Issue
In the future, describe your issues in detail (error messages, saves showing as corrupt, saves not loading, etc) so that people can offer advice. As of now, most people wouldn't know what the exact problem is.
That being said, I can tell you that a saveset for the original release won't work with the complete edition without some tweaking since they are recognised as being completely different games. What you'll need to do is extract the data file from the original edition save and inject it into a complete edition save. Thankfully, someone already wrote a brief tutorial on how to do this here.
Re: L.A. Noire Saveset Issue
I was having the same problem. Thanks for the link Dregen