As Neal Zaslaw has pointed out, writers on Mozart have often suggested—or even asserted—that Mozart never heard his 40th Symphony performed. Some commentators go further, suggesting that Mozart wrote the symphony (and its companions, #39 and #41) without even intending it to be performed, but rather for posterity; as (to use Alfred Einstein's words), an "appeal to eternity".
Modern scholarship suggests that these conjectures are not correct. First, in a recently discovered 10 July 1802 letter by the musician Johann Wenzel (1762-1831) to the publisher Ambrosius Kühnel in Leipzig, Wenzel refers to a performance of KV. 550 at the home of Baron Gottfried van Swieten with Mozart present, but the execution was so poor that the composer soon left the room.
There is strong circumstantial evidence for other, probably better, performances. On several occasions between the composition of the symphony and the composer's death, symphony concerts were given featuring Mozart's music for which copies of the program have survived, announcing a symphony unidentified by date or key. Copies survive of a poster for a concert given by the Tonkünstlersocietät (Society of Musicians) April 17, 1791 in the Burgtheater in Vienna, conducted by Mozart's colleague Antonio Salieri. The first item on the program was billed as "A Grand Symphony composed by Herr Mozart".
Most important is the fact that Mozart revised his symphony (the manuscripts of both versions still exist). As Zaslaw says, this "demonstrates that [the symphony] was performed, for Mozart would hardly have gone to the trouble of adding the clarinets and rewriting the flutes and oboes to accommodate them, had he not had a specific performance in view." The orchestra for the 1791 Vienna concert included the clarinetist brothers Anton and Johann Nepomuk Stadler; which, as Zaslaw points out, limits the possibilities to just the 39th and 40th symphonies.
Zaslaw adds: "The version without clarinets must also have been performed, for the reorchestrated version of two passages in the slow movement, which exists in Mozart's hand, must have resulted from his having heard the work and discovered an aspect needing improvement."
Regarding the concerts for which the Symphony was originally intended when it was composed in 1788, Otto Erich Deutsch suggests that Mozart was preparing to hold a series of three "Concerts in the Casino", in a new casino in the Spiegelgasse owned by Philipp Otto. Mozart even sent a pair of tickets for this series to his friend Michael Puchberg. But it seems impossible to determine whether the concert series was held, or was cancelled for lack of interest. Zaslaw suggests that only the first of the three concerts was actually held.