When he retired from writing and staging opera he remained a large influence on contemporary composers through his teaching. He taught vocal composition to Beethoven, Liszt, Schubert and others. He also worked with many prominent singers. all but the most wealthiest of students got their lessons for free, Salieri's way of repaying kindnesses shown to him when he was a young student.
Salieri composed very little instrumental music. A few concertos, three symphonies and a handful of other compositions. One of this handful was also one of his last compositions, the Variations on La Follia. It is for orchestra and is a culmination of everything Salieri had learned about orchestration over the years. Why he wrote it is not known, as it was written in 1815 long after he retired. Perhaps he just liked the Follia tune, maybe he was just inspired to do so. In any case, the music remains in the minor mode practically throughout and is rather somber. The Follia tune is always very recognizable in each of the 24 variations. It is the instrumental coloration of the orchestra and soloists that provides the variety. This piece remained the most monumental set of variations for orchestra until Brahms wrote his Variations On A Theme By Haydn in 1873.
As for the often repeated rumors that Salieri murdered Mozart (dramatized in the play and movie Amadeus) allow me to quote Chad Hille from his blog entry Antonio Salieri : Truth or Fiction on his blog Classy Classical:
"There is indeed no evidence to support the idea that Salieri killed Mozart. In Salieri’s last years, he suffered a physical and mental breakdown. He was admitted to the Vienna general hospital and the rumor spread that Salieri accused himself of killing Mozart. However, there was no concrete evidence of this. It would have been very unreasonable to think that Salieri killed Mozart. For during the times that the two great composers were both alive they were, for the most part, friends. Of course, there were times when the two did not see eye to eye. This was only natural as Salieri and Mozart came from different musical traditions and wrote in very different styles. On the whole, they got along with one another fine. It was even reported that Salieri came to visit Mozart on his deathbed. It is also reported that Salieri was one of the few who attended Mozart’s funeral. It is now widely accepted that Mozart’s cause of death was rheumatic inflammatory fever."
And that settles that, as far as I'm concerned.
Salieri's Variations on La Follia :