Honestly, I have been trying to find out the name for this effect for SO LONG, and I think I finally found it. Anyway, I think this visual effect can be successful in setting a specific mood for a film or scene of a film IF used appropriately. I have seen this effect used in the Matrix; I have used this effect for my horror film, the Book of the Mummy; and I will use this effect once again for my upcoming film.
The process for doing this effect is fairly simple: first, the video layer of a clip is duplicated a number of times; each duplicate, which must be above the original video layer, has a low enough opacity setting so that it allows all other video layers to be shown (I usually set the opacity of each duplicate to 50%); finally, each duplicate is shifted a number of frames to the right of the original video layer.