The current class design framework suggests a certain theoretical design space in which they can create new classes that are unique even before you get into particularly unique mechanics (like Mudra for instance).
- We don't have a melee casting class, which is a role that could be filled by Red Mage, Rune Fencer/Knight, or Blue Mage.
- We don't have a ranged physical class in the same "DPS tier" as Black Mage and Summoner. Something like this could work for Ranger or Gunner—these two may be unlikely given the existence of Bard and Machinist though).
- On the flip side, we also don't have a caster in the BRD/MCH "support DPS" role, though one could argue that the two of them now do themselves since they have cast times of their own. Geomancer might fill this role following their FFXI implementation, which was mostly about party buffs.
- Something like Dancer might work as a melee "support DPS," too.
- We don't have a Weaponskill class whose combos are completely freeform, by which I mean they can do their basic combo abilities in any order, producing different effects (think something like Mudra but with Weaponskills instead). This would be a way to differentiate Samurai from the other three melee.
- As others have mentioned, there's currently no class that manipulates TP the way that Black Mage manipulates MP (it wouldn't need to be an exact replica, of course, and shouldn't be, but the idea of a physical class with unlimited resources would still be somewhat unique). This might also be something for Samurai, given their focus on TP manipulation in FFXI.
Now, those are just ideas that fill some basic concepts that should be theoretically possible given the present design space. Some of them could be seen as reshuffling existing concepts (melee+caster, for instance) but that's generally what class design in RPGs is anyway. I would honestly say that they've covered a lot of mechanical ground in the present classes, though so in terms of innovative mechanics, I'm not sure where they might go.
We've seen defensive reactionary procs (Shield Swipe, Low Blow/Reprisal), offensive reactionary procs (Bloodletter, Firestarter/Thundercloud), resource manipulation (BLM and DRK), elemental cycling (Black Mage again), pets (SMN/SCH), limited "stack" resources (Aetherflow/Ammunition), slow-stack build to unleash something powerful (Wrath/Abandon), multiple "maintenance buffs" (Greased Lightning, Huton, Blood of the Dragon), high output healing (WHM) vs. barrier healing (SCH), and so on. Most of these sorts of things have analogues in other GCD-based themepark MMOs.
There are a few things we haven't really seen, such as a healer more focused on HoTs (such as WoW's restoration druid) or a healer focused on "spreads" (such as WoW's mistweaver monk). We've also not seen a healer that has "healing combos," though we have seen some healing procs.
So I would say that, in general, we're probably going to see most new classes be made unique through flavor and novel combinations of various party roles more than anything else. But the developers are also surely creative (I never would have predicted something like the Mudra system, for instance), so they could surprise us.