Actually I think 'Unfortunate' would have been the appropriate word in that song. Most of the situations described don't involve any direct negation of the protagonists intentions. The only possible qualifier is
'Mr. Play It Safe was afraid to fly
He packed his suitcase and kissed his kids goodbye
He waited his whole damn life to take that flight
And as the plane crashed down he thought
"Well isn't this nice..."'
... but the last line is still sarcasm, not irony.
Take an example of irony--the story of Oedipus. Oedipus leaves his family specifically to avoid a prophecy that he would kill his father, and marry his mother. The action of leaving his home, by which he intends to stop the prophecy by removing himself from proximity to his parents, causes it to come true, because unknown to Oedipus he was adopted. Oedipus causes the prophecy to come true by accidentally returning to his biological parents.
So we have the action of a protagonist causing the opposite effect of what was intended--irony. The items Alanis lists are mainly really annoying.
Alanis is a regional manager, overseeing several stores. Her office is located in a specific store. Alanis decices to institute a 'no smoking' policy on breaks for all stores, but not her own store (where her office is located - she loves to smoke cigarettes).
Corporate agrees and it becomes company policy. Impressed by Alanis's HR policy, they transfer her to an ailing store, where smoking is banned and she cannot undo corporate policy.
'Mr. Play It Safe was afraid to fly
He packed his suitcase and kissed his kids goodbye
He waited his whole damn life to take that flight
And as the plane crashed down he thought
"Well isn't this nice..."'
... but the last line is still sarcasm, not irony.