açılmış is also accepted; is the difference just that the sentence with açıldı suggests that the speaker saw it happen? I struggle with this, since you could conclude that the door was closed by seeing it closed, but you would not know if it had been closed slowly or quickly.
Yes, the difference is that the speaker witnessed it happen in açıldı and she didn't in açılmış.
Actually you could. If I come up to you and say, "Ruth, kapı yavaşça açıldı." and later on if you decide to report it to someone else you'd say "Kapı yavaşça açılmış", to convey the sense that someone else told you so, but you didn't see it for yourself.
There are actually two past tenses in Turkish: Duyulan (heard) Geçmis and Görülen (seen) Geçmiş. The heard past tense consist of -mış and the seen past tense consists of -dı. It's pretty self-explanatory actually, you use the heard one for things you didn't witness but instead heard it from someone else (or in some cases for things you realized after the event) and you use the seen one for things you did witness.
Wait so have I understood this correctly? Açmak is used when the action of opening is being done by the subject and Açılmak is used when the action of opening is done on the subject. So if we say kapı acıldı does it mean it opened regardless whether someone opened it or not? And Kapı actı would mean that the door did the action of opening(not necessarily opening itself)?
The meanings seem to be identical in some cases in English, but Açmak needs a direct object. Açılmak takes an indirect object (dative) only in special cases, like the door opened into a garden. http://www.turkishdictionary.net/?word=a%C3%A7%C4%B1lmak