A bill of goods, as a phrase, has two meanings. The less common is a delivery of goods, a consignment. The more common definition is something that is knowingly presented in a false way, usually with the intent to deceive or gain something by the trickery. The vast majority of the time it is used with the verb sell. Occasionally one will see the phrase with the verb buy.
Using the modifier false is slightly repetitive and isn’t necessary.
The plural is the awkward bills of goods. It is rare, perhaps because of its awkwardness.
A side note: One should be aware of a similar phrase clean bill of health. It means to have a medical professional examine someone or something and declare the patient to be free of disease or disability.
Charlie Hebdo and a whole tradition of scabrous satire are part of France, part of the French definition of freedom – and part of the bill of goods foreigners who settle there sign up for. [The Guardian]
Unfortunately, Chicago residents have been sold a bill of goods by officials who misrepresented a switch from coal to natural gas as ‘clean’ energy. [Huffington Post]
Every statement against the merger also applies to company’s smart meters, which are simply a bill of goods that policymakers have bought — or been bought by. [The Baltimore Sun]
The Central Bank of Nigeria, CBN, has given banks in the country a clean bill of health after running a stress test on the financial institutions. [Daily Post Nigeria]