Who was calling whom?
I watched this for the first time last night, then read some threads here and today started re-watching it with the various theories in mind. The thing that has struck me most so far in my 2nd viewing is a scene at the beginning, where the governess (Miss Giddens) arrives at the estate and thinks she hears someone calling the little girl (Flora).
I went back and listened to it several times. Even though the captioning says "Flora," none of the calls sound like that name. The first two sound like Mary and the last one perhaps Mara, i'm not sure, but to my ears it doesn't have an "o" sound. Also, it seems to be the voice of a young girl.
This is something i haven't seen speculated upon here, and as such maybe there is nothing to it, but it makes me wonder if Flora was calling out to Miss Jessel, the former governess. As in, maybe her first name was Mary or something similar. It could be that the first two calls were "Mary" and the third a combination of Mary and Flora, coming out as Mara (MARE-uh).
That is, Miss Jessel came to Flora after the second call and then they merged, and so too did their names. Yet Miss Giddens, being familiar only with Flora's name, heard it only as Flora.
Also, this took place near the lake where Miss Jessel had died.
Another thought is how the petals fell and Mrs. Grose said they were always falling. Flora obviously comes from flower and Jessel makes one think of Jezebel, depicted in the Bible as a fallen woman. Thus the white petals falling could symbolize that Flora was falling due to the influence (or possession) of Jessel. Another innocent fall, if you will, was Miles essentially falling to his death in much the same manner as Quint did. Ergo, Quint was the cause of Miles falling.
A final thought. Towards the end of the movie Mrs. Grose says something along the lines of how you have to be careful about waking a child from a disturbing dream, for the shock could be too much, thus foreshadowing Miles' death. This could also explain why Mrs. Grose didn't see the ghostly figure, in the sense that she didn't want to see it. For she had closed her mind to such possibilities, pushing them to the realm of dreams, thereby blinding her to the reality of what the waking world was showing her.
Addendum: I skimmed through more of the movie just now, having written most of this when the tv was otherwise occupied, for i remembered the graveyard scene where they looked at Jessel's tombstone. And voila, yes, it showed her name and it is Mary Jessel. Therefore the girl was calling out to her and when Mrs. Giddens asked Flora if she heard anyone call her (Flora's) name, she truthfully stated that she heard no one. To me, this definitely makes the movie a ghost story, for it doesn't make sense that Mrs. Giddens would have imagined the girl saying Mary/Mara but then asked her if someone was calling out the name Flora. In other words, it wasn't all in her mind. The girl was calling to the ghost. The children were possessed.
That, anyway, is how i see it.
I really didn't think i could come up with a good signature, but happily i thought of this one.