Versatile weapons cannot work with this feat.
There have been no errata to re-word the feat itself.
Flavor-wise, the feat only makes sense with big and heavy weapons.
You’ve learned to put the weight of a weapon to your
advantage, letting its momentum empower your strikes.
Rules-wise, the definition is perfectly clear.
Before you make a melee attack with a heavy weapon
that you are proficient with, you can choose to take a
-5 penalty to the attack roll. If the attack hits, you add
+10 to the attack's damage.
The feat is targeted at only STR-based characters, using both hands (as all Heavy weapons have the two-handed property). It is too flexible to be used with versatile weapons. Consider that you could drop something from your hand (like an Arcane Focus, or something else), attack with both hands, and pick the thing back up with your free-object interaction. This is even more imbalanced when characters have multiple attacks, advantage, and/or extra turns or abilities.
Eldritch Fighters could use their Action Surge to either attack several more times and re-equip the Arcane Focus for a War Caster AoO.
Multi-classing into Rogue-3 makes you able to use Fast Hands to equip a shield as a bonus action, so allowing you to have +2 Armor when your turn was done.
But maybe the most broken combo here would be Monks. Dexterity monks could now use a 2-handed DEX Quarterstaff with -5/+10 along with their unarmed strikes.
Any character with Haste (+2 AC, and an additional action)
I'm sure there are other cheesey combos out there that could be abused.
Consider also that you could now use this with weapons like the Quarterstaff, Trident, or Spear, which only do 1d8 damage (when used with both hands). Getting a +10 damage on a weapon whose maximum damage is 8 is a lot more valuable than with a weapon whose maximum damage is 10 to 12.
As a house-rule, I would not allow it. I very much enjoy the flavor, and the limitation, of the feat, requiring a big and heavy weapon to be used. My players are also power-gamers - I'm sure they'd exploit this somehow. When fighters and barbarians can pull off several attacks per turn with advantage, this becomes quite imbalanced compared with casters or ranged characters.
Best Answer
The PHB mentions Improvised Weapons, which do not necessarily belong to either category:
Natural Weapons (such as the Lizardfolk's jaws) are also a thing, and according to Jeremy Crawford they too are neither martial nor simple.
As enkryptor mentioned, some monsters use weapons that are not explicitly categorized.