Problems that could be potential interpretation issues:
SWAT Rifleman's Assault Rifle (presumably, he could use it)
Bad Cops' Shakedown (presumably, could be used)
5th Precinct Beat Cops' Clean Up the Streets (definitely think it could be used)
Hawkmen's Nth Metal Mace (definitely think it could be used)
Most of the really involved movement type powers on the Science Police and Hawkmen are, thankfully, tied to taking turns with them. This might not be an issue based on what we have.
But we'll need to watch future Common Lawmen additions very carefully.