It's a good thing the attacker(s) made the error of setting off a bomb next to hundreds of trained medical professionals. From the cops to the medical types at the runner's aid stations, there must have been a couple hundred people there within seconds who had some serious medical training for exactly this sort of thing. Heck, I even saw a couple of uniformed soldiers/airmen helping out (after they ripped down the crowd control barrier that was preventing assistance from getting in and out). From reports of the types of injuries sustained, a LOT more people would have died if they hadn't received medical treatment less than a minute after the blast.
How could other events be better prepared? We already see those automatic electronic defibrillators hanging on the walls all over the place, so how about some compact trauma kits anywhere large numbers of people gather? Based on the types of injuries we have seen in Iraq/Afghanistan from this exact type of improvised explosive device, they need nasopharyngeal airway tubes, battlefield compression bandages, battlefield tourniquets, quikclot gauze (magic stuff!), and gloves. Battlefield studies have shown that just those items can prevent up to 80% of "savable" combat casualties if used immediately, because people can bleed out or asphyxiate in just a matter of minutes, long before trained medical personnel usually arrive. The types of injuries sustained from these attacks are nearly identical to battlefield wounds. Put those supplies on the walls next to the AEDs, and you could save a LOT of people if this happened at a more typical large event with more people and fewer medical personnel who could respond in seconds. And it's pretty cheap too... Those items can last a long time if packaged properly.
If he has face/head/neck injuries but nose and facial bones appear intact, stuff the airway tube down his nose to behind his tongue.
If he is bleeding, apply compression bandage.
If he keeps bleeding, stuff in as much quikclot gauze as you can into the wound. Stuff in the whole package.
If he keeps bleeding, apply tourniquet.
If its in a spot that can't be tourniquetted, more quikclot, more pressure, elevate (unless its the head), and pray.
If he is bleeding from the chest and its bubbling, use the wrapper from the compression bandage directly on the wound to seal it up, tape it down if you have tape, and then use the compression bandage to hold it in place.
There is another category of injury that military members now get routine training for, pneumothorax. But that's some serious stuff poking people in the chest with a needle, and these relatively small terror bombs will probably only rarely cause a pneumothorax that can't wait until the ambulance shows up.