James Bone is shot twice in the opening sequence for the film.
Once while driving the Backhoe digger on the train. He is shot while rotating the Backhoe around 180 degrees. The shot hits him in the upper right shoulder, where he will later remove the shrapnel.
Eve shoots Bond while he is fighting on top of the train. The impact of the shot throws him off the train and into the river.
We know that James hear M announce to Eve to take the shot over the radio, but James is more thrown then jumps when the shot is taken. So it's doubtful that he faked being shot.
When James Bond falls into the river he goes over a water fall. During this sequence he hits the bottom of the water falls and sinks into the water. At this point you can see bubbles coming from his right side ribs. As shown in this image. I've circled the two locations where he has been shot.
In the opening credits of the film only one bullet hole is shown for the iconic imagery of Bond. This bullet wound is in the location where he was shot driving the Backhoe. The hole appears several times during the opening credits, in shadow figures of Bond and in a cardboard target of Bond.
Later in the film James Bonds appears shirtless, but sporting only one bullet wound.
In the interview sequence with the bad guy (sorry, forget his name, that's a movie joke). We are only shown one bullet wound, but M is blamed for the wound.
So this raises the question. Where is the second bullet wound caused by Eve when she shot him on the train?
It appears only once in the film, the moment when he hits the water. You can see two distinct injuries on Bond's right side. One in his shoulder, and one in his ribs.
Later in the film. Eve and Bond are discussing the shooting that went wrong. This happens just after he enters the new underground base for MI5. He tells Eve the shot only "cost me 3 ribs". Yet, later in the film we see him shirtless without any wound in that area.