Among the big questions at the start of this set of hearings is how much of the trial should be held in secret and who has the power to censor statements made in court.
At one point in Monday's session, the audio feed through which reporters listened to the proceedings went dead during statements that military officials said may have contained classified or sensitive information.
James Connell, a lawyer defending suspect Ali Abdel Aziz Ali, told reporters after Monday's session no one - including the judge - appeared to know who cut the feed.
“The judge expressed surprise that the security device had been activated," he said.
Judge James Pohl called for a clarification of who is allowed to censor court statements. The court then went into a closed session.
Monday's incident was an example of the snags that the military court is encountering in the U.S. government's efforts to present the trial as one that is open and fair.
The U.S. came under international and domestic criticism for trying the men in a military court on this base in Cuba where some argued they would not be offered the same rights they would have if the trial was held in a civilian court on U.S. soil.
U.S. military court officials are under pressure to be open and transparent, while at the same time dealing with evidence that is, in some cases, classified.
For example, one of the motions being discussed this week is a request by defense attorneys for the U.S. government to preserve the so-called “black sites” - facilities in third countries where the suspects were allegedly tortured after their arrests.
Victims' relatives who sat in on the proceedings have diverging views on whether the trial should be held in Guantanamo Bay as opposed to a civilian court in the United States.
Matthew Sellitto lost his son in the collapse of the World Trade Center towers in New York City.
“I think there'd be too much controversy back on the mainland - demonstrations, what have you. I think this is the proper venue," he said.
Phyllis Rodriguez' son was also killed in the attack on the towers. She believes the case should have been tried in federal civilian court, because she says having it far from U.S. shores is causing many Americans to ignore the proceedings and forget those who died.
“I feel it would have been much more open in federal court. The public would have had more access. The media would have had more access. You know, this is a trip to get here," she said.
Khalid Sheikh Mohammed - the self-proclaimed mastermind of the attacks - and four others were arraigned last May on charges including conspiracy and nearly 3,000 counts of murder.
One of the suspects, Walid bin Attash, fired one of his military lawyers. In an outburst on Monday, he complained to the judge that he sees no point in coming to court, because he says the government is placing too many restrictions on his defense and said he does not trust his attorneys.
The difficult start of these hearings is yet another indication of the complexity of the case and of how long the road to justice will be.
Twelve years after the attacks, the court appears nowhere near setting a date for the start of the trial.