Aren't they both considered correct? "Yesterday I watched a film" "Yesterday, I saw a film.'
Yes, they are both correct and in both cases the comma is optional. To watch something is to intentionally pay attention to it for some period of time. So certainly you "watch" a movie. To have seen something just means that the thing was within your visual field. "Seeing" something can be instantaneous and unintentional. You "see" the flash of a camera, but you don't "watch" it. In the case of "seeing" or "watching" a film, I don't think either of the words is preferred over the other.
In this case, let me first paraphrase Swan's "Practical English Usage" (#368):
See is used when to talk about visual impressions coming to our eyes; it's not always deliberate, might be accidental; seeing could happen without you thinking about it, or even without you realising that you've done it
Look (at) suggests intention or concentration
Watch suggests intention or concentration while looking at something that is happening, changing, moving, developing.
While we say "watch TV", we usually use "see" with public performances of plays and films
That being said: - you can watch TV, but you can't see TV (unless in the sense of, "I saw a nice TV in the store the other day" - in which case you can't really watch it).
you can both watch and see movies. In some cases, the watch version may imply more of a deliberate looking than the see version:
I saw 'Gone with the Wind' yesterday.
I watched 'Gone with the Wind' yesterday.
however, note that if you're talking about movies you have seen at some point in the past (ie., you have watched them, and now you know what they're about), then "I've seen 'Gone with the Wind'" would seem a bit more natural to me than "I've watched 'Gone with the Wind'".
finally, if you're talking about watching a film/movie N times, you can say both "I've seen 'Gone with the Wind' 5 times" and "I've watched 'Gone with the Wind' 5 times" (and the same goes for sentences of the type "I watched/saw X for the Nth time today"), and which version you choose here is up to you.
I would say that it depends on context. It comes back to the question of "intent" or "concentration".
So, I could say "I went to see a play". Intent (and presumably contration) are implied.
"I watched a movie." Could have been from the comfort of my own home, the use of the word watched implies intent and concentration. Had I gone to the cinema, I could have easily said "I went to see a movie".