Cryptic have stated that there are no BO's with skills outside the normal level, so no Beam Overload III at Ensign level slot. Any rarity above common has a chance to have one or more skills at level III, though I have not seen any noticable difference in which skills are effected between the rarities (so both an uncommon and a very rare might have Viral Matrix III for instance)
The rarity effects the number of traits that have a higher strength, so a Very rare officer might have Superior Telepathy and Superior Aggression, while a rare might only have one superior, and an uncommon might have one superior with another skill reduced to a Basic levelled trait to balance it out. They will not (afaik) have traits that their race doesn't already have a chance of possessing, and, apart from Saurians (and alleged Aliens, not confirmed) will not have space traits (saurians have a chance for Efficient)
Question about Bridge Officer's - Does their rarity only affect Ground Traits? In examining Rare BO's they seem to have some Superior ground traits, eg Superior Health.
Does it effect Skills at all, like are there any rare BO's that might have a commander level skill at an Ensign or Liutenant Commander level?
I don't believe that rare bridge officers have abilities at lower rank than normal. They can, however, have abilities that are not available from the bridge officer trainers or from player training, such as Aceton Field III, for example.