We actually do have a safe search setting (turned on by default). You'd be shocked to see what the results look like if you go into your settings and turn it off :)
As far as old vs. new site. The organic links should be the same, let me know if you are seeing differences.
The Videos tab at the top is a little different in that it's being populated pretty much straight from Youtube right now. On the new DDG you'll see similar results as you would here: http://www.youtube.com/results?search_qu...
Adding more filtering to the top area is a good idea and something we can hopefully look into in the future.