To be “sharp as a mashed potato sandwich” is not to be sharp at all—that is, to be dumb. “Sharp as a mashed potato sandwich” was teen slang from at least 1944. “Sharp as a mashed potato”—minus the “sandwich”—has been cited in print in the 2000s.
 
 
30 December 1944, Troy (NY) Record,  “The Young Idea” by Mossler (comic strip), pg. 6, col. 7:
(Parent talking about a teenager—ed.)
“It’s getting so I don’t know whether to sock him or treat him to a movie…he’s just told me I was ‘sharp as a mashed potato sandwich’!”
 
21 November 1946, Los Angeles (CA) Times, “Dyer Deserts His War Horse—but Climbs on Again,” pg. 8:
Honest, Al, by comparison the TroJan quarterbacks look about as sharp as a mashed potato sandwich.
   
Google Books
Proverbial Comparisons and Similes from California
By Archer Taylor
Berkeley, CA: University of California Press
1954
Pg. 72:
As sharp as a mashed potato sandwich.
 
20 March 1958, Traverse City (MI) Record-Eagle, “Spring Hasn’t Exactly Sprung,” pg. 1, col. 5:
The Weather Man, struggling to rise to the occasion of a new season’s advent, was about as sharp as a mashed potato sandwich.
 
4 January 1964, Wellsville (NY) Daily Reporter, “Red Ryder” by Bob MacLoed (comic strip), pg. 4, col. 5:
THAT’S A SMART IDEA—‘CAUSE RIGHT NOW YOUR SHOOTIN’ EYE IS ABOUT AS SHARP AS A MASHED POTATO LEAD PENCIL!
 
Google Books
Developmental Reading in Middle and Secondary Schools:
Foundations, strategies, and skills for teaching
By Lawrence E. Hafner
New York, NY: Macmillan
1977
Pg. 150:
He was as sharp as a mashed potato sandwich.
 
Google Books
Play It Again, SAHM
By Meredith Efken
New York, NY: Steeple Hill Books
2009
Pg. 21:
Was going to say, “She made you look about as sharp as a mashed potato.”
   
Google Books
Nothing Happened and Then It Did:
A Chronicle in Fact and Fiction
By Jake Silverstein
New York, NY: W. W. Norton & Company, Inc.
2010
Pg. 56:
“He’s about as sharp as a mashed potato.”
 
Texas Monthly
Texas Sayings
Anne Dingus teaches you to talk Texan.
by Anne Dingus
Dumb
Another great saying tied to Texas’ love of the land. Expressions for “stupid” are the second most common in Texas lore.
(...)
Sharp as a mashed potato.