there's some parts where you don't want to be at night. just stay on or around the well-lighted streets and you'll be fine.
Street Art Guide LA - Art District Los Angeles - a live guide through the streets of Downtown Art District
People shoot a lot of movies, videos etc, here, so you're bound to bump into some kinda of production, or closed street ;)
Enjoy my introduction to the neighborhood http://www.amoeba.com/blog/2009/10/eric-s-blog/the-arts-district.html