The Nicholls fellowship is probably the best screenplay competition out there. Very prestigious if you get into the top 100 you're pretty much garunteed someone big is gonna wanna read your stuff. It's tough though.
BBC are great, one of the only major TV film companies still to accept unsolicited work. Again, they get thousands of scripts a year, they take months to get back to you and it's usually a standard rejection letter, although I have had notes from them before.
Both tough nuts to crack, but great website full of great advice. I would read them front to back if I were you... and probably was once, and I did just that! You'll learn alot from them.
Here's a couple of links to my own blog that might help you:
Questions you need to ask.
Just a couple of thoughts that might help.
My best piece of advice is this, don't send your script out until you're 100% happy with it. Don't send it out thinking "I really should fix that line, that character, that typo, but I just want to know what they think!" Fix it, it wont take long and you'll have no regrets or doubts, you'll know you did the best you could. That extra hour, day, week, will make all the difference.
Best of luck.