Approximate matching in table of integer vectors
You are asking for the near neighbor problem for the Jaccard index. If you are ok with some approximation and randomization, I think there exist subquadratic algorithms based on Locality Sensitive Hashing (LSH). LSH schemes based on MinWise independent hashing are known for the Jaccard index: see the LSH survey by Andoni and Indyk and references therein, plus the LSH webpage (which has some code, although I am not sure if there is any for Jaccard specifically). Also see the original MinWise hashing paper.