1 - You'll need an edge. Why do I want to use your service over Youtube or Video or DailyMotion or etc... What makes your product better then established services?
2 - IF you get a foot hold in this category and actually become a popular service, you'll need massive infrastructure. You can of course, use AWS S3 to store the videos, Elastic Transcoder to process them, etc... but now your spending money you may or may not have. Video is quite different from photos. Their often big, consume huge amounts of bandwidth and 1 size does not fit all, nor do browsers play well with all the video formats. So either you need to design your own video processing that does a better job then everything else (which is possible, though daunting) or figure out how to make money really quickly.
3 - If the first 2 don't stop you, there is always the cat and mouse game of they have dozens if not hundreds of developers working on these sites and you have maybe a handful at the beginning. They may (or may not) be able to deploy new features much quicker then you can. So theres a constant lag in functionality.
Personally - I'd say find a niche. What kind of user is not being served? I really hate that now a days, almost everything is a 3rd party service. Build me something I can deploy to my own servers. Build a youtube competitor that via a few AWS scripts, can deploy to and utilize AWS services and I can have my users upload their videos directly to my own servers. That puts me in control of my content, where it resides and bypass what happens if and when one of these services closes their doors.
So - could you build a competitor? Sure! Should you? How much time and money do you have?