Players frequently get returned to the game in the very next down, as Stewart Bradley did. This isn't safe and isn't nurturing to the player. Stricter regulations to counteract the teams primary motive of winning can help.
Defense knows if you want to take a ball-carrier out, take their head. Stricter policies regarding targeting players head is a minor step towards improving players safety. This has been the NFL's current focus and so far it has shown little change.
Concussions become much more dangerous when experienced in succession. The best treatment for a person that has experienced a concussion is to rest and ensure that no further damage occurs while the brain is still experiencing swelling. Many concussions occur during practice. By reducing the number of allowed practices between games we can allow a player more time to recover.
A player that experiences a concussion also has pressure to still perform. This is one reason as to why many players deny having concussions. For his team and for his career. Creating policies that stop a player from receiving punishment for admitting to a concussion is a step towards players taking their physical safety more seriously.
Add a mediator that is not bound to the league. The mediator is there to regulate and ensure the safety of players and has the power to remove players that should not be playing.
Take the human out of the equation. Players commonly don't want to sit out. By embedding sensors such as accelerometers into the helmets of every player a networked view can be monitored to provide data about the force at which a hit occurred. This will allow players to be pulled based off a metric rather than an inaccurate concussion test.
Most people don't realize that football helmets are only certified to protect against neck fractures. There is currently no helmet that claims to help against concussions, for players in any league. This worthy invention is still on the world's wish-list.