I partially dislocated my shoulder doing BTN presses. Luckily, I healed up in a week or two. According to my doctor, any time you have your hands behind your head, you're putting your shoulder joints in a vulnerable position. I never have any problems doing front shoulder presses.
If you can't get the bar down to your chest, you need to work on your arm flexibility or use lighter weights. It wasn't easy when I first started, and I had to use lighter weights than the half-pressers at my gym, but using a full ROM on presses has paid off in terms of strength and size. IMO, not going all the way down on a press is as bad as not touching your chest when you're benching.