In "Lamb to the Slaughter," what are some ways that Mary Maloney could have been caught?

This is a super fun question, because imagination is your only limit.  

Let's start with the highly unlikely.  Mary could have been caught, if she confessed to her crime in front of the police.  That's not completely impossible.  After all, that's what happened to the narrator in the "Tell-Tale Heart."  His guilty conscience got the better of him, and he confessed.  Mary might have felt the same way and confessed her crime.  It's not likely though since she was giggling at the fact that the detectives were eating the murder weapon.  

"It's probably right under our noses. What do you think, Jack?" And in the other room, Mary Maloney began to laugh.

I think a more likely possibility for her capture though is a thorough medical examiner combined with a nosy neighbor.  The medical examiner would be able to narrow down the time of death to a small window. A nosy neighbor might have seen Mary leave the house to go to the store and marked the time.  The detectives would then be able to combine those two facts, and they would realize that Mary had to be home at the time of Patrick's death.  In fact, a nosy neighbor isn't completely necessary.  The detectives could check out Mary's alibi and get a rough timing of the situation and realize that Mary was likely home when Patrick was killed.