I don't really have anything to add about the bagged dried stuff.. but I can tell you that the 'straight out of the ocean dripping with salt' stuff is by far the best 'green' additives I've ever tried, salt and all...
We don't rinse it at all, just let it get on with rotting down (it pongs quite eye-wateringly at first, if you use great heaping loads of it, but breaks down quite rapidly).
I've not tried it as a slug deterrent mulch.. but I must say that's a really appealing idea.. and the next time we're out the cabin, I'm definitely going to try it... I fight the slugs every blessed year and the slugs almost always win...
Seaweed is said to be a 'green' compost additive, though I've also seen it listed as a 'brown' since the ratio of carbon to other nutrients in its makeup is high... *shrug* whatever.. it rots into lovely compost and that's all that matters in the end I guess =)
I'm assuming that your bagged seaweed should have some usage direction type instructions on the bag... I'd go by what they say... If it's dried and pulverised/powdered, then I'd use it sparingly as an additive. If it's just seaweed-y bits and bobs, I'd use it more as a top dressing/mulch type thing.
Good luck!
Annie in Norway