“Surgeons can bury their mistakes, but we architects have to cover ours with ivy” is usually credited to architect Frank Lloyd Wright (1867-1959). Wright gave a 1931 Art Institute of Chicago lecture, “To the Young Man in Architecture,” where he stated:
 
“The physician can bury his mistakes,—but the architect can only advise his client to plant vines.”
 
However, the architect/vine saying is much older than the 1931 lecture.  “Vines That Are Useful: They Help Cover the Mistakes of Architects” was published in the New York (NY) Evening Post in 1913.
 
A popular joke was first cited in 1948:
 
“George Heister points out that architects cover their mistakes with ivy, doctors with sod, and brides with mayonnaise.”
 
The last line (regarding covering up food mistakes) is sometimes given as “brides with sauce” or “chefs with cheese.”
 
[This entry was assisted by the pioneering work of the Quote Investigator and This Day in Quotes.]
 
 
20 May 1913, Springfield (MA) Daily Republican, pg. 4, col. 5:
VINES THAT ARE USEFUL.
They Help Cover the Mistakes of Architects.
[From the New York Evening Post.]
Some day the American institute of architects will get together and vote a solid gold medal, summa cum laude, to the man who invented vines; for it was he who made the architect’s profession safe. Architects, and especially builders who are not architects, make mistakes about as often as not; and the awful thing about it is that their mistakes have to be right out in plain sight, unless they can be hidden by vines and trees. It is dangerous and criminal to call in the help of the arson trust—for, while burning down your neighbor’s house, you may set fire to your own—and so vines find their most important function, a function which is more important even than producing champagne.
   
Google Books
Two Lectures on Architecture
By Frank Lloyd Wright
The Art Institute of Chicago
Chicago, IL: The Lakeside Press, R.R. Donnelley & Sons Company
1931
Pg. 62 (“To the Young Man in Architecture”):
9. Abandon as poison the American idea of the “quick turnover.” To get into practice “half-baked” is to sell out your birthright as an architect for a mess of pottage, or to die pretending to be an architect.
10. Take time to prepare. Ten years’ preparation for preliminaries to architectural practice is little enough for any architect who would rise “above the belt” in true architectural appreciation or practice.
11. Then go as far away as possible from home to build your first buildings. The physician can bury his mistakes,—but the architect can only advise his client to plant vines.
   
19 July 1948, Northwest Arkansas Times (Fayetteville, AR), “Try and Stop Me” by Bennett Cerf, pg. 4, col. 3:
George Heister points out that architects cover their mistakes with ivy, doctors with sod, and brides with mayonnaise.
 
Google Books
Native Stone
By Edwin Gilbert
New York, NY: Bantam Books
1957, ©1956
Pg. 4:
And he couldn’t help smiling as he thought of the old saying: Doctors bury their mistakes — architects plant ivy.
 
Google Books
Handbook of Humor for All Occasions
By Jacob Morton Braude
London: Bailey Bros. & Swinfen
1958
Pg. 57:
Architects cover their mistakes with ivy, doctors with sod, and brides with mayonnaise.
 
25 January 1958, Dallas (TX) Morning News, “Down to Earth” by Dr. John F. Anderson Jr., pt. 1, pg. 1, col. 1:
SOMEONE has said that architects cover their mistakes with ivy, doctors with sod, brides with mayonnaise.
 
Google News Archive
27 November 1959, St. Joseph (MO) Gazette, ‘Daily Astrology” by Rita Del Mar, pg. 8, col. 3:
Today’s Quotation: “Architects cover their mistakes with ivy, doctors with sod. and brides with mayonnaise.”
 
Hathi Trust Digital Library
Google Books
Building design for the physically handicapped. Comprehensive plan for the U.S. Capitol grounds. Hearings, Ninetieth Congress, second session, on H.R. 6589 and S. 222 ... [and] H.J. Res. 914 and S.J. Res. 74 ... March 19, 1968.
Washington, DC: U.S. Government Printing Office
1968
Pg. 108:
I recall to you that Frank Lloyd Wright used to say:
“Surgeons can bury their mistakes, but we architects have to cover ours with ivy.”
 
Google Books
Construction Failure
By Jacob Feld
New York, NY: John Wiley & Sons, Inc.
1968
Pg. 3:
For many years he has felt that one of the worst indictments of his own profession is in the statement; “Doctors bury their mistakes, architects cover them by ivy, engineers write long reports which never see the light of day.”
 
Google Books
20,000 Quips & Quotes
By Evan Esar
New York, NY: Barnes & Noble Books
1995, ©1968
Pg. 383:
Architects cover their mistakes with ivy, doctors with earth, and brides with sauce.
   
Process and Control Today
Young Engineers Needed To Continue Our Way Of Life
2 July 2007
(...)
To conclude - on a lighter note - may I remind you that it is said that architects cover their mistakes with ivy, surgeons bury theirs, but engineers, if they make mistakes, have to put them right.
 
Twitter
Erik Sentell
‏@senrik
Architects plant ivy on their mistakes, doctors bury theirs, and it seems chefs cover theirs with cheese.
6:48 PM - Jan 14, 2011 from Central Business District, Seattle