Least worst is the most emphatic and expressive. (see post #2) It suggests that it seemed to you almost like the videos were part of a competion to create the worst version of the song.
Also: I like ''this is the least worst'' or ''this is the least worst (worse?) video''
but I don't like
"this is the least worst I could find."
In other contexts, or if you wish to use more restrained (and, possibly, more 'correct') language: 'It was the best of a (very) bad bunch' , 'This video isn't much good, but it was the best I could find. They were all pretty awful.' (But the following could be confusing: 'All the videos were bad but this was the best': you are expecting to hear 'worst')
I don't like its use in the results I see in a web search; maybe it has become a part of a jargon?