The following link provides a letter to the editor by Robert H. Romer who writes,
In a 1994 "question" in this journal, Neuenschwander asked whether anyone had yet met Feynman’s challenge of pro- viding an elementary proof of the spin- statistics theorem... In spite of the importance of the spin- statistics theorem and the attention that has been devoted to it, the physics commu- nity still waits—probably in vain—for an elementary proof.
I currently face mixed answers on our understanding of the elementary proof of the spin-statistics theorem. Romer's letter suggests to me that we still do not fully understand how to prove the spin-statistics theorem from first principles. Does Romer's letter still stand true today, or has there been a recent publication that outdates Romer's letter?