Uh, it's very easy to mess that up actually. Putting the gun in your mouth and pulling the trigger could just lead to to it going out the back of your neck and not hitting anything important.
Apparently at least a couple of the other conspirators had the same problem; when the SS showed up at the door, they tried to shoot themselves but botched it and were arrested anyway.
Still, it says a lot about the film's historical accuracy and attention to detail that they don't actually show Beck killing himself with one shot - it cuts away from him just as the gun goes off, so the whole "two bullets followed by a coup de gras" thing could still be implied to have happened off-screen. In fact, if you watch the scene closely he's holding the gun at an odd angle to his temple, which may have been done deliberately to suggest he's not going to get the job done.
They said in the audio commentary, showing him failing to kill himself twice would have looked ridiculous - even more so in the context of the whole movie, I assume. Cutting away was the best choice.
Yeah, showing the way it really happened would have been a bad choice. But with the way the scene was filmed (and the awkward way Terence Stamp's holding that pistol) it's open to interpretation - you can choose to believe that the movie version of Beck took himself out with one clean shot, or assume the (much messier) historical version took place after the scene change.