There are too many variables which makes it impossible to find out post with maximum likes and shares. However most of the time readwriteweb, mashable and boingboing report about specific posts going viral under headline "internet is broken due to". However in reality a lot of controversial posts also get deleted or the person gets banned despite getting large number of shares. And that makes it harder for other social media monitoring companies to keep tab on such data.
Some of the instances where posts have gone viral. A person from New york shared his inbox conversation with his girlfriend cheating on him went viral with 185,215,734 shares. This post was shared on lot of pages across the world and groups. It was removed after 36 hours of being viral. The account of the person was removed too. That post got the maximum likes and shares but Facebook policy violated in this context so the person account was removed.
Similarly you can check accounts of Dan bilzerian, superwoman, nicole arbour to see how their posts are going viral in larger numbers.
Accounts getting closed, post removal and private sharing of post stops the actual data of shares and likes being miscalculated. Especially private group sharing or private share among friends doesn't get recorded in the list of shares. This is the reason a lot of data remains miscalculated.