Nothing makes an audience groan like a coincidence that doesn’t have a believable explanation. Except maybe for the Mr. Creosote scene in Monty Python’s “The Meaning of Life.” That was nasty.
In one script that I read, a woman who grew up believing that she was an orphan, found out that her mother might actually still be alive. She got an old picture of her mother and set out to try to find her. One night, she was talking with a friend of hers at a bar and a man approached them. The man said that he was waiting for a blind date and asked if it happened to be one of them. It turned out that he was in the wrong bar altogether, so he decided to head home. Before leaving, the woman told him that she was looking for her mother and showed him the picture of her. You guessed it – it turns out that the woman in the picture was his mother too. If that had happened in an actual movie, the audience would have started hurling their Jujubes at the screen.
There’s no way that an audience will buy that kind of coincidence. There’s actually no way that an audience will buy any kind of coincidence, but especially not one that is several layers deep like that. The problem with coincidences like this is that they are just a convenient (and lazy) way to move the action in the direction that the author wants it to go. The author’s job is to make everything in the story both dramatic and believable, so you will need to present everything in your script in a way that the audience will believe.
If you ever have a coincidence or some other piece of not-quite-believable information in your script, then you either need to rewrite that section to present the information in a believable way or you at least need to set up the coincidence in advance. For example, let’s say that you want to write about a woman is looking for her mother, and you want the mother’s son to be living in the same general neighborhood. You could set up the fact that they live in the same neighborhood by showing us in advance that the mother chose an adoptive family for her daughter that lived nearby so that she could secretly keep an eye on her. Then the daughter could place an ad in the Village Voice looking for anyone who knows that woman, which the man could respond to. That’s believable. Not terribly dramatic yet, but believable.
If you really want to add an element of humor, the man could also reply to an ad from the singles classifieds at the same time, which he then gets mixed up, so he goes to the meeting with the protagonist thinking that it’s a date. But now we’re getting into unbelievable territory again, so it would be better to keep it simple.
The main point is that you need to ensure that every part of your story is believable or that you at least set up any questionable story elements in advance. Even then, you still need that story element to be believable, but audiences can be pretty forgiving when you set up something like this for them.