The U.S. government is currently detaining hundreds of people indefinitely without charge or trial.

[ProSense]

5. This

"In March 2011, President Obama issued an executive order that permits ongoing indefinite detention of Guantánamo detainees while establishing a periodic administrative review process for them."

...is technically correct, but the executive order was in response to Congress cutting funding and prohibiting the closure of Guantanamo:

January 7, 2011
President Should Follow Up Today’s Signing Statement By Closing Guantánamo And Ending The Indefinite Detention Of Prisoners There, Says ACLU

WASHINGTON – President Obama issued a signing statement today sharply criticizing provisions in the National Defense Authorization Act (NDAA) that bar the use of Defense Department funds to transfer Guantánamo detainees to the U.S. for any reason and hinder transfers with Defense Department funds to foreign countries for resettlement or repatriation. Although the president signed the NDAA into law, he indicated that he will seek legislation to reverse the provisions and oppose any attempts to expand them in the future.

In a letter sent to the president on January 5, the ACLU pointed out that the NDAA provisions barred use of only a narrow section of government funds and the president can and should assert his authority to use non-Defense Department funds to transfer the detainees.

The following can be attributed to Anthony D. Romero, Executive Director of the ACLU:

“President Obama is correct that Congress should not be attempting to bar the administration from using government funds to transfer Guantánamo detainees to U.S. soil for prosecution or to transfer them to foreign countries for repatriation or release.

“But even with today’s signing of the Defense Authorization Act, President Obama still has the ability to transfer Guantánamo detainees away from the notorious prison. There is nothing stopping the president from ordering the Department of Justice or Homeland Security to send planes to Guantánamo to transfer detainees to the United States for prosecution or to foreign countries for repatriation or resettlement, and he should do so as soon as possible.

“The unlawful detention of Guantánamo detainees for almost nine years without charge or trial is a stain on America’s reputation and should be ended immediately. If the government believes there is credible evidence against Guantánamo detainees, it should bring those detainees to the U.S. for prosecution in the American justice system. Our criminal justice system has a successful history of prosecuting hundreds of terrorism cases while both protecting national security interests and upholding constitutional rights. Where no credible evidence exists, detainees should be transferred to countries where they will be safe.

“Guantánamo must be closed as soon as possible and we must put an end to the unlawful policies that have been carried out there. It is high time to restore the rule of law.”

http://www.aclu.org/national-security/president-obama-correctly-rebukes-congressional-attempt-hinder-transfer-guantanamo

Here is the Executive Order:

Executive Order 13567--Periodic Review of Individuals Detained at Guantánamo Bay Naval Station Pursuant to the Authorization for Use of Military Force
EXECUTIVE ORDER

PERIODIC REVIEW OF INDIVIDUALS DETAINED AT GUANTÁNAMO BAY NAVAL STATION PURSUANT TO THE AUTHORIZATION FOR USE OF MILITARY FORCE

By the authority vested in me as President by the Constitution and the laws of the United States of America, including the Authorization for Use of Military Force of September 2001 (AUMF), Public Law 107-40, and in order to ensure that military detention of individuals now held at the U.S. Naval Station, Guantánamo Bay, Cuba (Guantánamo), who were subject to the interagency review under section 4 of Executive Order 13492 of January 22, 2009, continues to be carefully evaluated and justified, consistent with the national security and foreign policy interests of the United States and the interests of justice, I hereby order as follows:

Section 1. Scope and Purpose. (a) The periodic review described in section 3 of this order applies only to those detainees held at Guantánamo on the date of this order, whom the interagency review established by Executive Order 13492 has (i) designated for continued law of war detention; or (ii) referred for prosecution, except for those detainees against whom charges are pending or a judgment of conviction has been entered.

(b) This order is intended solely to establish, as a discretionary matter, a process to review on a periodic basis the executive branch's continued, discretionary exercise of existing detention authority in individual cases. It does not create any additional or separate source of detention authority, and it does not affect the scope of detention authority under existing law. Detainees at Guantánamo have the constitutional privilege of the writ of habeas corpus, and nothing in this order is intended to affect the jurisdiction of Federal courts to determine the legality of their detention.

http://www.whitehouse.gov/the-press-office/2011/03/07/executive-order-13567-periodic-review-individuals-detained-guant-namo-ba