Well with a swing saw, at least as far as I understand them, it should be possible to saw most logs to grade fairly well. Maybe not 100%.
As Deeker pointed out, you'll likely have a hard time making a good profit with basic dimensional lumber, since there are big commercial mills that can crank out half a million board feet per shift or more. You'd probably have to get contracts with local builders and contractors to make that really pay. Though, in that case, the lumber would NEED to be grade stamped to meet code, so that's something else that you might need to consider. On a similar note, I know a couple local contractors/builders whom I've talked to about milling 2X6 Douglas Fir posts once I get my bandmill set up. They said if I can deliver for the same price or lower than they pay the building supply, they'd buy whatever they needed from me. They do use a fair amount of them for things like carport/garage support posts and the like. I also asked one of them about making the little 16" cross-braces they use between floor joists to stabilize them and he said the same thing. These could be milled out of small edgings and scraps - might not be really time-efficient money, but I could use ANY money about now, so these are just ideas I've been tossing around myself. I'm in about the same situation as you, though I don't have an operational mill other than my Alaskan as of yet.
As noted the money is in custom cuts. There was an ad on Craigslist in a city near me a couple months ago from a guy looking for someone to mill him two custom pieces - one 28" wide by 20' long(no specified thickness) for a bar top, and another 36" X 4" X 12' for a tabletop. He was offering $1000 for them both, which I realize might be below going rate (not sure), but still would be good money since a guy could easily mill those two pieces in a day. Obviously didn't make sense for me, since I'd almost need to hire a flatbed truck to haul the pieces the 260 km distance, but if a guy was local and had the necessary equipment for large pieces, it would be a good job to take.