There's been some discussion about whether D.C. prosecutors should exercise their discretion not to prosecute Senator Webb's aide for possessing a gun in violation of D.C. law. But if, as Senator Webb says, the aide "completely inadvertently took the weapon into the Senate yesterday," in the sense of bringing in a bag containing the gun without realizing that it might contain a gun, then the aide is simply not guilty.
Generally speaking, one isn't legally guilty of criminal possession of an illegal item (whether guns, drugs, or what have you) if one (1) doesn't know that one is possessing the item, and if one (2) isn't even aware of a substantial and unjustifiable risk that one is possessing it. Mistake about whether possession is legally forbidden to you is generally not a defense. Moreover, if one thinks that one might well possess the item, but one doesn't investigate further (or, worse still, one takes affirmative steps to avoid learning the truth), then one would be guilty. But if a cab driver is handed a suitcase by a passenger to put in the cab's trunk, the driver is not guilty of illegal possession of a gun or of drugs stored in the suitcase (unless he is aware of the suitcase's contents, or at least suspects what the suitcase's contents may be). Likewise with an aide, if he really didn't know or suspect what was in the bag.
That's a broadly recognized legal principle, but there's even some specifically D.C. authority on point: See Campos v. United States, 617 A.2d 185 (D.C. 1992):
[A] person who has no knowledge that he or she has a pistol, despite the fact that it is located on his or her person, does not exercise direct physical control over the pistol [required for possession]. One cannot effectively exercise control over a pistol on his or her person unless he or she knows that it is there. Cf. Johnson v. United States, 309 A.2d 497, 499 (D.C.1973) (government must prove defendant had knowledge to establish possession). Similarly, a person cannot have the requisite intent to do the prohibited acts that "constitute the carrying of a pistol without a license" unless he or she knows that the object he or she is carrying is, in fact, a pistol. A defendant cannot possess the requisite general intent to commit a crime without "be[ing] aware of all those facts which make his [or her] conduct criminal."
Now I say again that if the aide knew or suspected he was carrying a gun, he would be legally guilty even if he, for instance, thought there was some statutory exception for Senators' aides. In that situation, the prosecutor would have to exercise his discretion in deciding whether or not to prosecute. And of course even if the aide says he didn't know or suspect he was carrying a gun, the prosecutor would have to decide whether he believes the aide (though that's not usually what's called "prosecutorial discretion"); and it may well be that the Senator's vouching for the aide will tip the scales on that point, so I'm not claiming that if charges against the aide are dropped, that decision will be entirely independent of who the aide's boss is. Nonetheless, if the aide really "completely inadvertently" brought in the gun, in the sense of not knowing or suspecting that there was a gun in the bag, then he's just not guilty. And a prosecutor who believes that the aide just didn't know what was in the bag should therefore drop the charges.