Why did Bruce Banner grab the scepter?

Bruce Banner is a man with, as Tony Stark says half in jest, "breath-taking anger management issues".

Although not really demonstrated all too much in the Marvel Cinematic Universe, Bruce Banner is a man with multiple reasons to be angry at his own existence - he has a mostly uncontrollable monster within him at all times, he's constantly terrified of injuring people and he's been forced into hiding by various US Government agencies, distancing him from the people he loves. In the comics, it's been demonstrated that he has some deep psychological problems and self-esteem issues (see The Ultimates), and that he had trouble with his anger before he first turned into the Hulk.

So when Bruce Banner realises that;

• Loki is trying to use him (specifically, a part of himself that he resents) in part of a plan to take over the Earth
• the people he has been bonding with for the last day or so are terrified of what he could become
• Fury is using the Tesseract to create weapons of mass destruction

all in the space of a few minutes, he begins to show some of the anger that he tries to keep under control.

We find out in Avengers: Age of Ultron that Loki's sceptre contains one of the Infinity Stones, the Mind Gem, which is capable of manipulating people's emotions and fears, at least to some degree. Its proximity to the group of arguing people is no coincidence - during the scene in question, the sceptre is slightly glowing as the camera focuses in on it, indicating that the sceptre is beginning to make people more rash then they otherwise would be, demonstrated perfectly by the increasingly heated argument between Steve Rogers and Tony Stark.

As such, Bruce Banner gets more worked up than usual, to the point that he ends up picking up what he knows to be a very dangerous weapon without even seeming to realise it. When he later turns into the Hulk and roars, we see Loki react to the noise with a sly, self-satisfied grin, indicating that this was all part of his master plan.

It all comes down to the idea that Bruce Banner has very little control over his emotions, so when his emotions are amplified by a magical sceptre, he acts irrationally and without thinking. It's there to demonstrate that Bruce Banner is quickly losing control of his emotions, raising the tension for the audience and the characters in the room - because we all know what happens when Bruce Banner gets angry, and you probably won't like it.