Why couldn't Otonashi of Angel Beats pass on? Everyone in the anime 'passes on' after coming to peace with the life they used to have, except for Otonashi. Unless I'm really confused, Angel seemed to imply that the reason Otonashi couldn't pass on is because when Otanashi was alive, he was an organ donor who gave away his heart.

This explanation doesn't make sense to me. Does that mean that all organ donors are stuck in limbo like Otonashi?

Why couldn't Otonashi find peace/pass on to the next life?
Otonashi did pass on, although he was the last to pass on. He is assumed to have reincarnated at the end of episode 13, the final episode of Angel Beats, and it is heavily implied he meets the reincarnated version of Angel. 

The reason why he couldn't pass on just yet was not fully explained, but we can try to form a conclusion from it, so it is not entirely speculative. First, he lost all of his memories and so he has to regain it to truly understand what he regretted. He did not end up in the afterlife normally like the other students had, so it's highly possible that he did not have a regret in the first place. It could be that he was in that afterlife in order to have Angel move on with her life, as she regrets not being able to give thanks to the person who gave her heart. Kanade, the Angel, was there before him and that normally wouldn't make sense since he died before her. 

Another explanation is that he simply regrets not being able to achieve his dream of becoming a doctor or more specifically, to help people. He wanted to help people after his sister's death and because he died before he was able to reach his goal, it's understandable that he regrets not being able to see for himself that he saved a life. Once he sees that Kanade was able to live her life, that she was content with the life he gave her, he was able to move on shortly after. 

I don't think all organ donors would necessarily have regrets. If they lived a full life, they would not be stuck in this afterlife school in the first place. Remember that you will only be in this afterlife if you have regrets. Otherwise, you would presumably just be reincarnated. Just because you donated your heart doesn't mean you get to be stuck in that limbo.



Sources:


How is it possible that Kanade has Otonashi's heart?
Wikia: Yuzuru Otonashi - Another Epilogue