Arsenic & Old Lace feels like a very well constructed stage comedy to me, but I was reflecting last night on the fact that it starts up with three coincidental events.
Yes, yes, spoiler alert in case you don't want to know!
In one evening:
1) Mortimer proposes to Elaine
2) Mortimer stumbles upon a corpse in his aunts' house
3) Mortimer's murderous brother Jonathan arrives at his aunts' house
Granted, there's a slight connection between 1 and 2. Mortimer has been spending more time at his aunts' house lately because Elaine lives next door. So his interest in Elaine makes it more likely that he will discover what his aunts have been up to. But, basically, 1 & 2 are a big coincidence.
There's also a kind of connection between 2 and 3, in that the play suggests there's a streak of homicidal mania that runs in this family, and the aunts and Jonathan are both afflicted. But, again, basically, 2 & 3 are a big coincidence.
Coincidence is just events coming together without a direct causal connection. There's nothing wrong with them, as such, in a story. The usual advice is to place them early in the story, to make them part of the "intractable problem build-up" and not part of the "surprising-but-logical solution". And that's what's going on here. The 3 events are just piling up to create a state of total humorous crisis for Mortimer, who I would say is the "hero" of the play, even though the "lead characters" are his aunts.
A lot has been written about including coincidences in a story. A storyteller makes a kind of bargain with the audience, a bargain whose terms are specified as the story goes along. The audience commits time and attention to the story, and expects a payoff of some kind at the end.
When the tale's completed
the audience shouldn't feel cheated.