Mljet to Korcula

For ferry schedule purposes, there's no shoulder--just high and low, so May is low season. If Jadrolinija does not list one I think you are out of luck. Someone will correct me if I'm wrong, but I think Jad is the only one doing that route.
(Korcula Ferries is a good resource: http://www.korculainfo.com/ferries-korcula.htm)

That sounds right for Dbv-Korcula too, but note you can take the bus too--which I much prefer, especially if you will be taking other ferries later.

Jadro does the LONG dist routes, and thats of course mainly seasonal
ALL isles have year round car feries to nearest mainland, and often a buslink using them, or at least to/fro ports, which may be just a jetty in the wilds. hecne can go every day, several times, Dub-isle.
as you can also read in any good guidebook

getting there not the problem, getting there and back to Dbv or on to Korcula on same day is the problem

Once again: Boats timetable valid up to 31.8.08: www.korculainfo.com/ferries/catamaran, www.jadrolinija.hr
As far as I know, there are no other ferries.

Hi - we're going to Dubrovnik, Mjlet and Korcula in May as well and based on my (I believe) comprehensive research, there doesn't seem to be any ferries between Mjlet and Korcula in May. It only kicks in in July. Also, yes, I believe the Jadrolinija ferry only runs on Thursdays and Sundays in May from Dubrovnik to Korcula. & I think that's the only ferry route to/from the two places.