He captioned the snap: "Finally dot it right! How do you make a mistake like that?" he joked, before blaming a Morse code translator he had found on Pinterest for the spelling mistake."
Orlando - who is engaged to pop superstar Katy Perry - also included a picture of another new tattoo featuring the name and an image of his dog on the inside of his forearm.
He added: "Fortunately I know how to spell Sidi. Forever my boy."
Fans first spotted the mistake after the film star shared the original ink dedicated to Flynn - who he shares with ex-wife Miranda Kerr - which also features his date of birth and the time he arrived into the world in January 2011.
Orlando captioned the post: "new #tattoo can you guess who? (sic)"
Shortly after, the tattooist - whose Instagram handle is @balazsbercsenyi - posted his own snap of the ink, and added: "A beautiful reminder for @orlandobloom of his son and yes, a dot is missing, we know, it will be fixed :) (sic)"
He later uploaded another snap after correcting his mistake and wrote: "Round 2 with @orlandobloom + we added the missing dot to the morse code, and did a small one in memory of Sidi, his dog + conclusion: never fully trust what your clients find on pinterest + Life is officially back to normal (sic)"