Late last month, The Daily Beast identified a digital media start-up that created a limited liability company (LLC) to buy political advertising. The Atlantic reported Wednesday that the LLC bought somewhere between $1.2 million and $4.6 million of political advertising over about five months. But the name of the start-up, reportedly backed by LinkedIn co-founder and Executive Chairman Reid Hoffman, never showed up in the political ad archive because the ads were paid for by the LLC it owned.

Facebook announced in May a new tool to promote political advertising transparency on the site. But a series of news stories over the past few weeks reveal that political advertisers are exploiting loopholes in Facebook's system to obscure the source of their funding.

In a separate incident, a Virginia congressional candidate was the subject of a series of nasty attack ads with a disclaimer that said the ads were "Paid for by a freedom loving American Citizen exercising my natural law right, protected by the 1st Amendment and protected by the 2nd Amendment," The New York Times reported Wednesday. A Facebook spokesperson told the Times that the ads were allowed under current policy. Facebook told CNBC Thursday it is working on ways to verify the people or groups who are mentioned on political ad disclaimers.

"One of the important aspects of the ad archive is the meaningful transparency it provides," Facebook spokesperson Andy Stone told CNBC in a statement. "Now political and issue ads that run on Facebook are available and open for public scrutiny so that voters, journalists and researchers can all ask questions about who is behind those ads."

The act of obscuring political ad funding is nothing new. Political action committees, commonly known as PACs, are allowed to collect money outside of a particular campaign and spend it on ads of many kinds, including TV, radio, direct mail and digital. But regulation around political ads online remains ambiguous.

In March, the Federal Election Commission proposed two sets of rules that would regulate the disclosure of campaign financing on websites and apps as well as how disclaimers would appear in small digital ads. But The Washington Post reported in late June that the rules would be unlikely to come into effect before the midterm elections.