Do any armchair lawyers (I know, I get what I pay for) want to chime in on the legality of creating user-definable 3-5 second gifs of YouTube videos, which link back to the video in question, for an online video curation library thing?
With a good DMCA takedown story and compliance, you could potentially claim the copyright is responsibility of your users. And maybe you'll be too small, and the content, in general you are making too inconsequential, or even helpful (marketing wise) for anyone to care. But this is definitely be a project I would get a proper legal analysis of and have clear procedures and plans in place for any issues that may show up.