i disagree, i think that if you cut, edge, trim, then blow off the lawn will look much better. ive found that if i edge and trim before cutting the tire of the mower wrecks the nice line that the edger and trimmer make.for instance when you edge first then cut along a sidewalk, the tire of the mower rides right on the edge line making it not look as sharp.
you obviously cant do this when grass length is very long because like some others said the mess left from trimming and edging is picked up by the mower, but for me even in the spring on a 7 day cutting cycle i have no problems with a mess of grass left when i mow first.
just what works for me, may not work for everyone.
The grass is always greener on my side of the fence.