Should those responsible for bringing the case be disciplined?
Not for bringing charges in the first place. Though the affidavit of probable cause appears to have contained claims the prosecution knew were false or exaggerated. They should be held accountable for that if it can be proved.
As for the actual conducting of the prosecution, there were a couple things that the prosecution did that absolutely merit disciplinary action, and perhaps even disbarment. First, the prosecution tried to withhold the text messages that the IT specialist recovered from Martin's phone. Those texts were clearly exculpatory, in that they showed that Martin had experience and skill in fighting, which would tend to make it more plausible that Zimmerman was on the bottom (which was a material factual issue in dispute). The IT specialist blew the whistle on this Brady violation, and the defense got the evidence - but not until just before trial. The judge then denied a continuance that the defense requested in order to properly authenticate the texts, and then excluded the texts as evidence because they were not authenticated (applying the wrong legal standard for authentication in the process). That alone would have been solid grounds for reversal had GZ been convicted. Oh, and the IT guy who called out the prosecution for withholding the texts from the defense? Angela Corey fired him for doing it. Expect a lawsuit over that. It will not just be forgotten.
Then there was the child abuse/felony murder ambush. The state had an argument that had clearly been in the works for weeks at least (and it was still pathetically weak, but that's neither here nor there). But they didn't give the defense a heads up. Not that a heads up would have mattered, because 5th Amendment Due Process requires that the prosecution specify from the outset what statutes the defendant allegedly violated. They can't just have a trial and then decide what to charge. (Manslaughter as a lesser included is different, because murder 2 requires all the elements of manslaughter plus malice, which means there is no element of which the defense did not have fair notice.) The idea that the state must specify the charges in advance is one of the most fundamental principles of constitutional criminal procedure. Apparently none of the prosecutors were paying attention when they taught that in law school. Or they just didn't care.
In addition, the prosecutor tried to claim that the predicate felony of child abuse consisted of the very act of pulling the trigger, which is not allowed either, though this screw-up is perhaps more a matter of pathetically bad lawyering than one of prosecutorial misconduct. The predicate felony must be separate from the act of killing, or else the two merge into a single charge of murder or manslaughter. Otherwise, every manslaughter would also be felony murder, because in every homicide you can say that the perp killed the victim while committing the felony of killing the victim. Any first year law student would know this, so it is difficult to believe the prosecutors were not aware that their argument was completely frivolous. And springing it on the defense that morning, when it had clearly been planned for some time, is just another indication of how dirty and underhanded the prosecution's handling of the case was.
Ms. Corey ought to be very concerned. Not because she pursued charges in the first place, but because of how the prosecution (at her direction) conducted the case. I would not be at all surprised if she is severely sanctioned.