Going to failure set after set means progressively sloppier form which definitely will stress the joints/connective tissue more and leave you more prone to injury.
Regarding shoulder pain, many times this is due to poor benching technique. Check out the video in this article for proper bench form, that should help the shoulder:
To avoid elbow pain, don't go too heavy on arm work, stick with lighter pumping movements, unless you are very warmed up. But even then, I wouldn't go to heavy, if you are hitting the chest and back hard you are already getting some good stimulation for the triceps and biceps.
I'm with Charles, I prefer to do more sets. I'd rather steer clear of failure, execute each rep flawlessly and explosively and do many sets of low reps. It has worked great for me. I am currently 33.