I wonder why they are so late. They should have arrived a long time ago.
Does this sentence have two possible meanings? How would we choose between them?
1) I expected (predicted) their arrival would have taken place a long time ago.
2) It would have been better for them to arrive much earlier, maybe they have missed something at the party.
The ambiguity is real, but in practice will be overcome by context.
In the context of I wonder why they are so late the natural interpretation of should is epistemic referring to probability or expectation: your 1).
I wonder why they are so late. They should have arrived long ago. I hope nothing's happened ...
But it in another context the natural interpretation might be deontic, referring to obligation or advisability: your 2).
What a pity they're arriving now. They should have arrived a long time ago, when we were having fun. Now the party's started breaking up.
And then of course it's possible that both meanings are intended.
What a pity they're so late. They should have arrived a long time ago, when the party was rocking. Gosh, you don't suppose something's happened to them?
Lots of words in English have multiple possible meanings. Usually you can tell which is meant from context. Usually the intended meaning is so obvious that the reader does not even pause to think about it, he just naturally infers the correct meaning. It is certainly true that writers sometimes slip up and have one meaning in mind, but write a sentence in which the intended meaning is not clear.
For example, the word "trunk" can mean, 1) the main body of a tree, 2) the storage compartment of a car, 3) a large suitcase, or 4) the nose of an elephant. If I wrote, "We went to the zoo where my children were delighted to see the elephant blow water out of his trunk", I don't think anyone would think for a moment that I am talking about the trunk of a car. But if I read, "Bob accidentally backed his car into a tree. The trunk was badly damaged", I'd guess the writer means that the trunk of Bob's car was damaged, but he might mean that the trunk of the tree was damaged. The sentence was poorly worded to leave such an ambiguity.
Many jokes are based on such ambiguities: The reader is set up to think that one meaning is intended and then suddenly an alternate meaning is sprung. Like:
"My job requires me to travel a lot."
"Oh, does your wife miss you much?"
"No, she's got a deadly accurate overhand."
Or consider the delightful pair of sentences:
Time flies like an arrow. Fruit flies like honey.
This throws you off because it uses a double ambiguity. In the first sentence, "flies" is a verb meaning "travels through the air"; in the second it is a noun referring to a type of bug. In the first sentence "like" is a preposition meaning "as" or "in the manner of". In the second it is a verb meaning "enjoy" or "favor".
