The Old Guard (Situational Irony)
We see that all of the white employees from the former President's administration are packing up to leave, expecting to be fired now that Mandela is President. Surprisingly, Mandela invites them all to be part of his administration so long as their desire is for the good of the country and its people. Mandela subverts the expectation that he will simply replace the old administration with people who agree with him, and shows that he is more committed to the project of unity and shared vision.
Family Relations (Situational Irony)
Mandela is an exceptional leader, compassionate and forgiving, able to bring people from disparate political backgrounds into his orbit to work towards a common goal. Ironically enough, he has a harder time creating unity within his own family, as his wife and children see his project of compassion as foolish, given all of the political unrest in the nation and the unhappiness it has brought their family.
Springboks wins (Situational Irony)
A central irony in the film is the fact that, in spite of the fact that the Springboks team starts off playing horribly and no one thinks they have even a remote shot at doing well in (let alone qualifying for) the World Cup, they end up winning a definitive game against the record-breaking and seemingly unbeatable New Zealand All Blacks team.
Mandela picks Francois (Dramatic Irony)
There is a brief instance of dramatic irony in which Mandela looks in the newspaper at a photo of Francois and the Springboks. We the viewer see that he has a plan to ingratiate himself to Francois, but none of the other characters are aware of it.