I use an air compresser to dry it off, but aluminum doesnt rust anyway(well it oxidizes instantly but thats a whole chemistry thing), so the worst thing that can happen if you dont dry it, is that you will have some water spots to wipe off. (unless you use some of that clear dry stuff). Only steel parts are probabaly the shafts, outdrives etc. and usually they are blued or chemically treated to prevent corrosion anyway.

One thing to watch though, if you have one of those new stainless steel lined dishwashers that heat up to like 200*F, you may not want to use the dry cycle at all, just pull it out and shake it off, use an air compressor or towel if you like.
Dishwashing detergent is designed to remove food greases(polar), and it works just as well on other hydrocarbon type oils and grease.

and I forgot to mention, if your diffs arent sealed, seal them up with some tape or something if you can. I seal mine with silicone when I put em back together and use sealed bearings, so no probelm there for me.