One of Buffy's classic comedy episodes - something this show did particularly well, most of them were hilarious - in 'Bewitched, Bothered and Bewildered', Cordelia dumps Xander on Valentine's Day and he tries to get his revenge by persuading Amy the witch to cast a love spell on Cordelia, so that he can hurt her the way she hurt him (Xander is not actually that nice a character sometimes, though he is very noble when Buffy comes on to him under the influence of the spell). Of course, it all goes horribly wrong.
The reason the spell goes wrong is that Cordelia is already in love with Xander and has only broken up with him because her friends were teasing her, so the spell rebounds off her and onto every other woman in Sunnydale - or, as Giles suggests, because Amy got it wrong and Cordelia's necklace, which she used in the spell, protected her rather than targeting her. Or, perhaps, the reason it goes wrong is that Amy calls on entirely the wrong ancient goddess for her spell. Amy's spell invokes 'Diana, goddess of love and of the hunt'. Diana (Greek Artemis) was indeed goddess of the hunt, but she was not the goddess of love - that was Venus/Aphrodite. Diana, like Minerva/Athena, was a virgin goddess, and therefore extremely unlikely to help someone with a love spell. Perhaps Marti Noxon, the writer, thought Venus was a bit too obvious and would distract the audience by calling to mind the many, many uses of Venus as goddess of love in popular culture in everything from pop songs to bridal couture to women's razor blades. Still, she could have used the goddess' Greek name, Aphrodite.
This is not the only spell Amy casts in this episode. As she and Buffy, both under the influence of the first spell, fight over Xander, Buffy uses her Slayer power and hits Amy, and Amy responds by using her witch's power to turn Buffy into a rat. The specific spell is, 'goddess Hecate work thy will, before thee let the unclean thing crawl!' Hecate continued to be used for transformation spells throughout the series, for Amy's second attempt in this episode, on Jenny Calendar, cut off by Xander ('Quit with the Hecate!'), for Amy's own transformation of herself into a rat in 'Gingerbread' and for Willow's brief attempt to turn a high school student with an enchanted jacket (yes, really) into a woman in 'Him'. This is more appropriate since Hecate, a minor goddess existing on the fringes of ancient religion, was the goddess of witchcraft. The ancient Hecate doesn't have a particular connection with transformation, metamorphosis or transfiguration - she was associated primarily with ghosts, necromancy (in Greece and Rome, this meant raising the dead to get them to make prophecies) and the night. For spells relating specifically to metamorphosis, I think I'd have been inclined to go for Circe, the divine witch (daughter of a sun god and a nymph) who turns sailors into pigs in the Odyssey. However, Hecate is appropriate enough, since she was goddess of witchcraft in general and that would include metamorphosis, as it does in the Odyssey and in Apuleius' Metamorphoses (also known as The Golden Ass).
Buffy used Latin and classical references for magic spells very frequently - it's something of a go-to ancient language for the show, something I talk about at more length in a paper that will be published online soon. Greek occurs much more rarely, presumably because it's a less well known ancient language, though it is used for the name of the oldest vampire, 'Kakistos' - the worst of the worst (in season three's 'Faith, Hope and Trick'). It is used there to emphasise Kakistos' extreme age, as Greek is probably older than Latin, and the best known part of Greek history predates the best known parts of Roman history.Greek is better known and more acessible that the oldest languages, Egyptian, Akkadian or Sumerian, while still emphasising that Kakistos pre-dates Latin and the Romans (Dawn claims to have learnt Sumerian in season seven, which given the difficulty of Sumerian and the amount of time she's been around is extremely unlikely).
In this episode, however, the spells are in English rather than Latin, because rather than incantations in which the words, in the appropriate language, produce the magical effect, these are actually prayers to pagan goddesses asking the goddess to produce a magical effect. Both forms of magic spell or incantation were used in Greek and Roman magic. Perhaps goddess-magic appealed because magic in Buffy is strongly associated with women and femininity. For all Willow's mocking of the group she meets with at college in 'Hush', who are all about feminine power and baking cakes, there are very few male practitioners of magic in Buffy - one metaphor for a drug dealer, one warlock and Giles and Ethan, who don't generally self-identify as warlocks or wizards (Ethan does, to an extent, but he's drunk at the time!). This episode is about romance and about Xander inflicting something on the women of Sunnydale (none of whom are too pleased with him afterwards) and Amy, the witch, has gained her magical power from her mother, who was also a witch. And, of course, the ancient deities of sex and love from many cultures are almost always goddesses, probably because they start out as fertility goddesses, and it seems logical for a fertility deity to be female. So, although Noxon has misidentified the goddess of love, it probably seemed natural for these spells which are connected to love and to what these women will do for love to come in the form of incantations invoking goddesses.
The invocation of Hecate for transformation is one of the few fairly stable spells in Buffy - although love spells and vengeance spells appear quite often, they tend to be different every time. Hecate may have been re-used partly because the rat transformation spell, which was re-used in season three, was so specific, or perhaps just because this (very good) episode and its spells were particularly memorable. It certainly helps that the language of the spell is English and therefore easy to remember and follow! Other ancient deities appear from time to time throughout the series, interspersed with spells of the magic-words type, but Amy's dark-eyed, glowy invocations of Diana and Hecate are certainly among the most notable.