RDM should absolutely have healing skills. Sure White Magic has also usually included some damage dealing, but the RDM has black magic and weapons for that. The benefit of RDM's white magic has been healing/buffing. It wouldn't feel right to me if RDM wasn't chucking a heal occasionally.
Of course pure heal GCD skills on a DPS character are pretty much wasted unless you make it such that their DPS does not suffer for it. So make them oGCD or some kind of oGCD buff that adds healing effects while you still do damage or whatever implementation that doesn't get in the way of DPS. Doesn't have to be more than a couple skills, just make them fairly useful generally and/or clutch.
(The healing magic problem is the main reason I thought RDM would make a neat tank, White Magic = damage reduction CDs and a panic heals button. Oh Well!)

Outside of that? Well RDM should really not have "high level" magic spells on their own. I think the sort of theme should be combining their weaker magic and physical prowess in fun ways to do damage. It'd be fun, for example, if they had fire 1, blizzard 1, aero 1, and cure 1 but had combos and things so end up working very differently than the BLM/WHM versions.
And Dual Cast has to be important to them somehow.