In "The Cask of Amontillado", is there any particular significance to the fact that Fortunato is a mason?
Obviously, it gives Montresor the opportunity to mock Fortunato, by playing on the double meaning of the word 'mason', but is there any deeper importance?
Yes, but only to a point is the mention that Fortunato is a Mason a significant detail. Masons have secret handshakes and codes of conduct relating to other Masons. It is against the Masonic code to harm or lie to a brother Mason. When the Montressor failed the "mason test" by producing a trowel, Fortunato should have figured out that he was being lied to and made good his escape.
Fortunato made the secret sign to "ask" if Montressor were a Mason, and he seemed not to understand rather than make the corresponding "reply" sign that yes he was a Mason. Fortunato made the sign because he felt uncomfortable going into the damp and underground catacombs with Montressor. If Montressor were a true Mason, Fortunato could trust his life in the hands of his "brother Mason".
I think Poe uses an interesting play on words in that the Masonic organization and the brick masons use the same symbols and tools. Masons meet in secret, and the narrator has Fortunato in a secret place in the catacombs. Montressor uses brick and mortar to seal up Fortunato because of an insult. Many Masonic symbols deal with stone or brick work.
Poe mainly chooses the word to stress its double meaning, but the reader could also infer that Montresor uses it because it has some connection to the wrong that Fortunato supposedly did to Montresor. Perhaps Montresor desired to be a member of the secret society, and Fortunato helped block his admission to the "club." It could also be that Montresor is so jealous of Fortunato that he uses this opportunity to demonstrate that he can do something that Fortunato is good at (masonry). These are all speculations, but they could be supported by other parts of the story.