OP what you witnessed, I would no way ever say anything to another parent about. It is simply none of your business. If she was a close friend you could strike up a conversation about bribing and threats and if they really work, but as a complete stranger it is just socially wrong to ay anything about a different parenting style.
As for spanking in public, I would tell the parent that what they are doing is inappropriate and they need to stop or go do it in private.
Julia, mama to Bumpa 2008, and The Mole 2011