You're overlooking an important difference between exposing film to light and sharing a poem. In the first scenario, Mark has damaged Jack's property, and frankly I suspect he'd be considered the primary responsible party even if he weren't trespassing (unless Jeff tricked him into damaging the film).
Not at all. Ordinarily, people have a reasonable expectation that they can turn lights on and not break things. If he wasn't trespassing, he has done nothing wrong, the responsibility would be wholly on the person who left the vulnerable film in an area where it could easily and innocently be exposed to light and who then allowed people into that area.
However, when we trespass, we assume liability for any damage we do because the trespass itself is the predicate wrongful act. You can leave our valuable painting on the table to dry. If you invite someone into your home and they spill soda on it, they can argue you shouldn't have left it there and invite them in. But a trespasser can make no such argument and so is responsible for the damage. For liability to exist, the person has to do something negligent or willfully damaging. Turning on a light in a house you were invited into is neither.
In the second scenario, Mark has caused no harm to Jack; the only possible "wrong" in that situation would be the violation of the contract between Jack and Jeff, but if he's trespassing, there's been no wrong committed at all because the contract hasn't been breached.
Of course if Mark actually caused no harm to Jack, then even though Jack did something wrong, Mark has zero damages and so no reason to sue. But assume for the sake of argument Jack can demonstrate actual harm fairly traceable to Mark's trespass. For example, say he had a publishing contract for the poem and the publisher backs out.
You have to accept those kinds of harms. Otherwise, I can spray black paint all over your Rembrandt and you have no damages. After all, it's still paint on canvas. The fact that other people will no longer pay as much for it or pay to see it has to be a recognizable damage.