You have to up the tessellation for all the 3 parts of the results from the fillet/trim (try 15 or so). This means the outer mesh, the fillet, and the inner mesh. You have to do this for every fillet trim. Also, be aware that this will only show up in a render....you'll still have the gaps in one of the working viewports (though I believe there's a box you can tick to view the tesselation there though it slows things down a bit).
Also be aware that this isn't correcting the geometry. If you want to get rid of the gaps, you'll probably want to convert to poly and start cutting and merging vertices to line things up.
"Terminat Bora Diem, Terminal Auctor opus."