@bubbers, of course you can still dispatch a 737 with an inop autopilot. You just can't enter RVSM as you need automatic altitude holding capability. So everything up to FL280 (in europe) is fair game.
@Prober, flying a non precision approach is nowadays exactly the same as an ILS, both in presentation and basic procedures on the 737. Read up on IAN which i believe is also standard in the 748 and 787. Apart from that i can't agree more. Regular manual flying is the only way to keep basic flying skills up, and i'm grateful that my companies OPS manual recognizes that and promotes raw data manual flight.