Obviously it depends on the country / regulator, but nothing in my airline. We fly MFF on A320-A321-A332-A333 and the first time I flew the A333 was just a regular non-training flight. A320>A321 was a powerpoint however.
The A333 is really no different. It's nicer to fly, more stable on the approach vs. the A332 which can be a bit 'pitchy'. Turbulence penetration is M0.78 vs M0.80, but we aren't encouraged to memorise those anyway due to MFF - they are printed on the back of the normal checklist in each aircraft. Fuel jettison is not installed on A333, it's a customer option on A332 anyway. Centre fuel tank is 'missing' on older A333s (it's actually physically present but not connected). Newer heavy weight ones have it activated I understand.
Can't think of much else!