In the synthesis, we made an alkene, then we added "Br2" across the double bond to make a vicinal dibromide, then we attempted to make the sulfone. Three people have now looked at the NMR, and the consensus is that the majority of the material has returned to being the alkene, which is surprising.
I am beginning to think that the proposed mechanism in the paper might not be correct. Perhaps the first step is displacement of the bromine on the primary carbon by the sulfinate anion, followed by elimination, and maybe the first step is slower when this attack must take place on a secondary carbon atom. E2 reactions happen more quickly at secondary than at primary carbons, which suggests to me that the reaction might not be E2 in whatever step controls the rate.