Unfortunately for the pseudo-certain grammar scolds who think they caught a pretty chick singer being stupid - which is such a satisfying thing for a certain brand of hipster male and his female enablers - the song does in fact contain irony.
The most obvious example is in this stanza:
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..."
And isn't it ironic... don't you think
Since we can be fairly certain that Mr. Play It Safe doesn't want to die in a firey plane crash, his thought "Well isn't this nice" is indeed ironic. The rest of the song contains dramatic and situational irony. The people who claim the song doesn't contain irony don't know the meaning of irony.
And so here is the Merriam-Webster definition:
iro·ny
Pronunciation: 'I-r&-nE also 'I(-&)r-nE
Function: noun
Inflected Form(s): plural -nies
Etymology: Latin ironia, from Greek eirOnia, from eirOn dissembler
1 : a pretense of ignorance and of willingness to learn from another assumed in order to make the other's false conceptions conspicuous by adroit questioning -- called also Socratic irony
2 a : the use of words to express something other than and especially the opposite of the literal meaning b : a usually humorous or sardonic literary style or form characterized by irony c : an ironic expression or utterance
3 a (1) : incongruity between the actual result of a sequence of events and the normal or expected result (2) : an event or result marked by such incongruity b : incongruity between a situation developed in a drama and the accompanying words or actions that is understood by the audience but not by the characters in the play -- called also dramatic irony, tragic irony