Should non-tenured/non-tenure-track faculty be permitted to vote on tenure-track hires?
While on the job market this last year, I talked with top departments that gave all their full time non-visiting members of the faculty a vote in tenure-track faculty hires. So there is definitely precedent.

Personally, I'm not thrilled by the shift at many universities to having a larger proportion of the active faculty be non-TT. But when this means that the responsibilities of non-TT jobs are similar, it is only reasonable that the rights should be similar too.

Benefits of doing so include all things that come from a work environment that is perceived as more democratic and where all faculty get a vote in determining the future directions of the department. The drawbacks are much less clear to me.