It wasn't normal for Dylan to use a lot of reverb. Most of his vocals were dry and close-miked, but heavily compressed once he went electric. I think that atypical effect was intentional in that song, to convey someone floating away on the verge of death.
Although now that I think about it, "Lay Lady Lay" was pretty reverberant, too. Maybe that was some producer's idea to give Dylan a more pop-sound.