Wrong? In what way? Isn't competitiveness the whole point of a race?
Without being particularly fast, I'm super-competitive when participating in events. I don't see anything wrong with it at all, quite the opposite really. I agree with Dylan - as long as good race etiquette and good manners are observed then it's fine.
I'd always stop to help someone in trouble though. A friend and I once stopped halfway through a trail marathon and got out the first aid kit to patch up a lady who had fallen off her bike. And if the person I was racing to the finish line fell over, I'd stop and help them up rather than run off and leave them.
