Jon, here is my research thus far on these talks.
***DISCLAIMER*** I wrote this back in the Spring. For those coming to this thread for the first time please read the whole thread. More evidence has been uncovered. This post is outdated!***Mrs. Patton, do you exist?
Many months ago it was brought to my attention that there was a story shared by President Thomas S. Monson that had some contradictions in it. These contradictions were seen because he had talked about the same story many years before. I did some research on the people mentioned in the story to attempt to discover the historical truth.
I was only able to discover the errors and so I share it with you. Perhaps there is someone who can offer an explanation to the contradictory story told in two General Conferences of The Church of Jesus Christ of Latter-day Saints.
The most recent version of this story is titled “Mrs. Patton-The Story Continues,” General Conference, October 2007.  The initial story was told in General Conference, April 1969. It was reprinted in the New Era, April 1991, and titled “Mrs. Patton, Arthur Lives.” This story has now been made into a Mormon Message and can be found here: http://LDS.org/church/until-we-meet-aga ... rs.+patton
In this story Monson talks of a childhood friend, Arthur Patton. He gives a physical description and says that Arthur “stood taller than any boy in class.” It is unclear whether Monson was in the same class as Arthur. Monson was born in August 1927 and Arthur is said to have been born about August 1925, a difference of 2 years. Arthur would have been a class or two ahead of Monson. Thomas Monson attended West High School in Salt Lake City, Utah from 1940-1944. The (Spring) 1938 West High Yearbook does not have an Arthur Patton as a student, but that is probably too early. The 1939 and 1940 yearbooks have not yet been scanned onto the schools website. A Classmates.com subscription granted me access to the 1939 and 1940 yearbooks. There is not an Arthur Patton in either of those yearbooks.
The story goes that Arthur joined the Navy in 1940 as a tall 15 year old. The US did not enter in to World War II until December 7, 1941. It seems unlikely, though not impossible, that a 15 year old would feel compelled to enter service in the Navy before the US even entered the war. The letter from Mrs. Patton indicates that he joined at age 15 which would have been anytime between August of 1940 and August of 1941.
There are contradictions between the two stories that were told.
In the first version, “Mrs. Patton, Arthur Lives,” it is claimed that Arthur Patton served on the Lexington and died in the Battle of the Coral Sea on May 8, 1942. The Lexington did sink on that day with as many as 300 lives lost. 
The follow up version, “Mrs. Patton, The Story Continues,” gives a different account. It is claimed that Arthur was lost at sea while aboard the USS White Plains at Saipan. A cited letter from Mrs. Patton contains the death date July 5, 1944. The USS White Plains was not in combat during that date. From Wikipedia, “The USS White Plains departed the combat zone on 2 July but, after a week at Eniwetok, returned to the Marianas with her air squadron upgraded to a total of 28 aircraft.” 
Clearly Arthur could not have lived both these versions of the story. One or both are false. If he was on the Lexington and died in 1942 then the follow up story along with the letter from Mrs. Patton are false. It does not appear that the second story can be true because the White Plains was not engaged in battle July 5, 1944.
In an effort to find out where US casualties were sustained on July 5, 1944 I have discovered that there were military personnel who died in France on that date. I am not a WWII expert and have not determined what battles were taking place or which branches of the military were involved.
There are lists available to look up the names of those who lost their lives during WWII. Arthur Patton does not show up on those lists. I have searched on a WWII casualty list through the National Archives as well as Ancestry.com and found an absence of the name Arthur Patton.  In fact, there is no Arthur Patton of Utah found in the WWII enlistment records searchable through Ancestry.com or Footnote.com. The WWII U.S. Navy Muster Rolls, 1939-1949 database on Ancestry.com does not contain an Arthur Patton. I found two “Patten” men from Utah who enlisted in 1944, neither one named Arthur.
What about the mother? Terese Patton of Pomona, California should be found somewhere. I did find a Terese Patton on the Social Security Death Index and the California Death Index, though not living in Pomona. She matches a Terese Patton on the 1930 US Federal Census for Chicago, IL that has a son Arthur Patton with the right birth month and year along with 3 other children. This Terese lost her husband on December 8, 1941 in Chicago, Illinois, the day after Pearl Harbor was attacked, and her 4 children are still living according to one Ancestry.com public family tree. It does not appear that this family lived in Utah any time prior to his death where she could have been a widow working as a cleaning woman. However, Terese's social security card was isued in Utah prior to 1951.
Monson describes Mrs. Patton as grey haired and shoulders “stooped from age.” That is not what most would expect of a description of a woman in her mid-forties.
This Terese Patton certainly does not fit all of the criteria.
The 1940 US Federal Census would perhaps give us more definitive answers as there would have to be a "Patton" family living in the Monson neighborhood for the story to work. However, we must wait several more months before that can be consulted.
One idea that I had was that maybe Monson changed the names to protect the family. This cannot be the case, however, since the mother is claimed to have miraculously attended a viewing of the conference with friends, recognized the story and wrote a response letter. Because the details of the ship and death were wrong in the first version the only other way Terese Patton would have been able to recognize the story as her own would have been the names.
In conclusion, the faith building story about Thomas Monson coming to the spiritual aid of a grieving widow named Terese Patton is not true as it has been given in General Conference. There was not a boy named Arthur Patton from Utah who was enlisted in WWII or a casualty of it according to the databases I've consulted.
1. “Mrs. Patton, Arthur Lives” LDS.org. http://LDS.org/new-era/1991/04/mrs-patt ... rs.+patton
2. “Mrs. Patton- The Story Continues” LDS.org. http://LDS.org/general-conference/2007/ ... rs.+patton
3. West High School Yearbooks website. http://west.slcschools.org/alumni/Publi ... rbooks.htm
4. Classmates.com West High School Yearbooks
5. USS Lexington Wiki page. http://en.wikipedia.org/wiki/USS_Lexington_(CV-2
6. USS White Plains Wiki page. http://en.wikipedia.org/wiki/USS_White_Plains_(CVE-66
7. Casualty page where “Arthur Patton” of Utah should appear. http://media.nara.gov/media/images/27/32/27-3134a.gif
8. Ancestry.com Public Family Tree. I have not verified information from this family tree.