With your reference to the Protection of Freedoms Act, can we assume you're referring to private parking charges, rather than penalties issued by councils?
The two main parts of it that affect parking on private land, and any associated parking charges, are
Chapter 2 and
Schedule 4. Section 54 of Chapter 2 made clamping on private land an offence. This created what some (particularly former clamping companies) described as a problem - as you'll probably know parking charges are governed by contract law, and the parties to any such contract are ordinarily the driver who parked, and the parking company. Without being able to clamp, there might have been no real way to enforce private parking charges, as the parking companies wouldn't know who the driver was, and unlike with S.172 requests, the registered keeper is under no obligation to name the driver.
Schedule 4 aimed to fix this perceived issue, by providing a mechanism through which any unpaid parking charges can be recovered from the keeper or hirer of a vehicle, providing certain conditions as defined in the schedule are met. The main conditions relate to the land in question ("relevant land" as defined by paragraph 3 - so as a common example, airport drop-off car parks are usually not "relevant land", being subject to statutory control in the form of byelaws, so no keeper liability), and the timeliness and content of the parking charge notice.
The reason you see it mentioned so much is that some parking companies don't bother with it at all, or try to comply and mess it up (quite how they manage this when they've had 12 years to get it right is anyone's guess), providing posters with a technical point of appeal.