The former President of Iran should never have said what he said about Israel and about the Holocaust in particular when he was president, and the new leader is much more flexible. The old one said what he said because he is his own crazy self and he is not going to apologize even though he should.
It could not hurt to be honest. I think that treating other countries and other areas of the world with respect is a good thing and it would be good for the people of Iran to see him apologize and regard Israel with respect and a friendly nature, overall it couldn't hurt.
Mahmoud Ahmadineja needs to apologize to Israel regardless of his status and especially now that he is not the president of Iran anymore. He did a lot of damage with the words he said and put a lot of people's lives in risk. The threats and other things he uttered upon Israel will require a more than an apology, but its a start.
I believe it is far better for Mahmoud Ahmadinejad to stay out of politics rather than come forward to publicly apologize to Israel in light of the fact that he is no longer the president of Iran. His loss of his position does not indicate that all is good and well between Iran and Israel anyway.
As a private citizen of the Iran Mahmoud Ahmadinejad is entitled to the opinions he holds and may have expressed in the past. While many of his alleged statements (it is contended that several of them are inaccurate translations) were offensive to the state of Israel he is entitled to hold and express those opinion. No apology is due!