I’ve been modelling a spaceship and when I render it with the model set to smooth, I see errors where parts are darker and lighter than they should be. I render with auto-smooth turned on. Here is a picture that shows what I mean, as well as one of the mesh.
Any help on how to fix this problem would be much appreciated.
Any time you’ve got anomolous light/dark faces, there’s a good chance your normals are backwards.
Select the face, F9 to get the correct panel, as shown in your second screenshot.
See the “Draw Normals” botton in the bottom right panel, “Mesh Tools 1”? Click that on, and depending on your scale, you can increase the “N(ormal)Size”. Rotate the view a bit and you can see which normals are sticking out (i.e. facing outward).
Most likely the bad face will have the yellow “stick” pointing inside the model. In the panel “Mesh Tools” click on “Flip Normal” and all selected normals will flip direction. If you have a simple model without “inward facing faces”, you can also select all and type Control-N to set ALL normals to outward facing. Might not work with some of your bevelling though.
I put draw normals on and all appear to be pointing outwards. I did Ctrl-N anyway and it made no difference. Here is what I see with draw normals on (in case I’m blind or something 
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Edit: Once you have clicked on the thumbnail, you have to click on the big image to get it to its full size, otherwise one of the normals will appear missing.
I am not sure but these triangles probably give you a strange topology. Try to erase them.
It looks like it was simply a matter of making the smoothing angle lower. There are other parts of my model that had similar problems, but I don’t have time to check them right now. Thanks for your help dgebel and neablo