"The authority to establish military commissions under chapter 47A of title 10, United States Code, as added by section 3(a), may not be construed to alter or limit the authority of the President under the Constitution of the United States and laws of the United States to establish military commissions for areas declared to be under martial law or in occupied territories should circumstances so require."

Comment:
What areas of the world are under U.S. martial law or are occupied territories?
Is Iraq or Afghanistan considered to be an occupied territory of the U.S.?

Quoting from section 5:
"(a) In General- No person may invoke the Geneva Conventions or any protocols thereto
in any habeas corpus or other civil action or proceeding to which the United States, or a current or former officer, employee, member of the Armed Forces, or other agent of the United States is a party
as a source of rights in any court of the United States or its States or territories.

Rearranging the phrases may help clarify:
In any habeas corpus or other civil action or proceeding to which the United States, or a current or former officer, employee, member of the Armed Forces, or other agent of the United States is a party,
No person may invoke the Geneva Conventions or any protocols thereto
as a source of rights in any court of the United States or its States or territories.

Comment:
Is the intent of Congress to protect all agents and personnel of the United States from mistakes they may make, even the ones whose actions put shame on our nation?
Doesn't this act remove our support for the Geneva Conventions and thus send a signal to others outside our nation that they too can ignore it?

Definition of terms:
Agent:
From Blacks: A person authorized by another (principal) to act for or in place of him; one intrusted with another's business.
From Wikipedia: a person authorized to act on behalf of another person.

Habeas corpus:
From Blacks: The name given to a variety of writs..., having for their object to bring a party before a court or judge.
From wikipedia habeas corpus is the name of a legal instrument or writ by means of which detainees can seek release from unlawful imprisonment.
Other links: lectlaw, The Columbia Encyclopedia and from Common Dreams

Access to Thomas
I have not determined how to link directly to legislative information from the Library of Congress as compiled by Thomas.
Therefore, the links above will take you to the search page.
Please type in the bill number, in this case S.3930
then select "Bill Number" and click on the search button.
Then, select the version, in this case "S.3930.ENR".
Then, select the section of interest, in this case "SEC 2" and "SEC 5".
If any one knows of a way to link directly to a section, please contact me.
Thanks!

Roll calls:
For the House H.R.6166 use roll call 491
or Senate S.3930 use roll call 259.