The behind the scenes reason is because Boba wasn't originally in ANH and that was Don Post, I believe, and not Jeremy Bulloch (you can also tell from the gut as Bulloch is slimmer, parts of ROTJ-Boba aren't him as well if I remember correctly) and was added for the 1997 special editions. And I guess someone just forgot to add the skull.

In A New Hope (Special Edition), after Jabba threatens Solo, we see Boba Fett - except he's missing his infamous skull insignia on his left shoulder pad.

Does anybody know if this was a movie goof or was there a reason they intentionally left it out? If they stuck him in there solely for fan-service, why neglect a major part of the costume?

the WORST goof to me was that in the SE edition of Ep. VI, in all the new scenes with Boba, his helmet antenna on the WRONG SIDE OF HIS FRIGGIN HEAD!!!!!!!   GAHHHHHHH!!!!!!!!!!!!!!!!   

makes me angery........  yet another sign that Lucas doesn't bother to really pay attention to our favorite character

On that one, they had to reverse the film for that because Boba was accidentally facing in the wrong direction. In order to make him face the correct direction they had to flip the film, which caused his antenna to appear to "move". A similar flip can be seen in TPM when they first reach Otah Gunga, you can briefly see Obi-Wan's padawan braid move to the other side of his head. And I believe Anakin's padawan braid moved sides once or twice as well.

makes me angery........  yet another sign that Lucas doesn't bother to really pay attention to our favorite character

1. stormtrooper hits his head in eppy 4
2. the infamous force kick from eppy 6
3. incomsistant shadown in cantina in eppy 4

what have you noticed