Direct Object. Is there a rule?

Solution 1:

The package fell a great distance

Subject + intrans. verb + adverbial phrase

It rained cats and dogs

Either Dummy subject + intrans. verb + real subject
or Dummy subject + intrans. verb + idiomatic adverbial phrase

For rain to be transitive, you would need a sentence like

The congregation rained confetti on the wedding couple.

Solution 2:

"Rain" can be either transitive or intransitive. In this case it is transitive.

In your "fell" example, "a great distance" is not the object of the verb, but an adverbial phrase. Consider the sentence, "Bob said nothing for several days." The object of "said" is "nothing". That is what he said. "For several days" is an adverbial phrase describing the manner in which he said it. Same thing here: "a great distance" is not what was "felled", it was how the thing fell.

By the way, "fell" can also be a transitive verb, though the usage is not common. You can say, "He felled a tree", meaning that he cut a tree down and made it fall.