QUICK-ISH, SHORT-ISH ANSWER:
The biggest, most obvious one is the use of Pegasus feathers to make the sail of the Jewel of the Realm (3.05). When Killian and his brother first journeyed to Neverland, they actually flew there using a sail made of Pegasus feathers. In Greek mythology, Pegasus was a horse with the ability to fly. So from that alone, we know Killian is from a land where the Greek myths are more than just myths.
Now… there’s a next logical step up from this, but the only thing about this particular assumption is that I’ve sort of been holding back on my theory regarding who I suspect is Killian’s mother. However, seeing as how this is a question regarding the Greek mythology surrounding him, I’ll bite. Going off of his last name alone (Jones) and his close association with the sea, as well as the fact that Pirates of the Caribbean is a Disney property (and when they did Dead Man’s Chest, the storyline involved a beating heart outside of a living man’s chest, which a lot of OUAT storylines seem to revolve around), I made the assumption that Davy Jones (a la POTC) was Killian’s father. From this point, it doesn’t take much to assume that the writers would pull from the exact same franchise to determine Killian’s mother. Going by that assumption, in POTC 3, we find that Davy Jones had an affair with the goddess of the sea, Calypso. So it’s because of this that I assumed she was Killian’s mother.
That assumption was sort-of solidified when I looked back at 3.05, and noticed two things—Killian’s profession within the Navy was that of navigator, and he accomplished this navigation via the constellations, so he was also an expert in astronomy. Calypso, according to Greek mythology (and POTC), was a sea nymph and the daughter of the Titan Atlas (who would be Killian’s grandfather). Atlas was the Titan charged with holding up the world, and was the titan of astronomy and navigation. So there’s that little factoid.
Now… I was going to wait until a larger post to talk about the house that I suspect belongs to Davy Jones (that he built for his son and Emma and Henry), but I’ll leave just this little tidbit here:
See that little statue I’m pointing at in the BTS shot? That’s the Greek goddess Pheme, and the statue is called “Winged Fame”. Here’s the description of the statue from a site that sells it:
Pheme was said to have spied on the affairs of mortals and Gods alike spreading scandalous rumors when wronged. She was usually depicted with wings and a trumpet. Here she carries off one she had spied upon who carries a broken sword showing how powerless her victim is to combat the rumors.
That’s the only clear thing from that house I’ve been able to distinguish. However, there are other pieces of imagery from that house that I find interesting—a painting of an island over the mantle (still trying to determine which one, suspect it’s Calypso’s), a painting of a lake with a swan and a sailboat in it, a statue beneath said painting, the nautical-themed furniture bearing swan’s heads. I’m going to do an additional post on all this later.
And one last thing… if Killian’s father is Davy Jones and his mother is Calypso, then that would mean that Killian is descended from both a mortal man (assumption) and a goddess, which would mean that Killian would actually be a demi-god. Kinda explains his whole penchant for survival, doesn’t it? ;-P
Thanks for the question! :-)