Okay, so a friend and I had an fight. Not a screaming yell-fest or anything, but a verbal no harsh words exchanged kind of fight. My friend is notorious for forgetting things, dates, appointments, and promises. He does try to remember, but fails. Another important detail is this is a universal thing, he does this with everyone, even his mom. The argument, he and I had was we had plans to see this show, but on the day of, I call him and ask "Where is he?" He responds that he is at a friends going away. I was pissed, so mad that I found it hard to speak on the phone. We talked, he apologize repeatedly, I told him that I forgive him, but that it hurts to be forgotten. We hit a point in the conversation, where he said that he would call tomorrow. He didn't. I want resolution to the situation, part of me wants to call him back and part of me wants him to call me? Which option would be better choice?

If he is this forgetful he may well have some medical issues or problems, does he not have a daytimer or a schedule on his phone to put down important things,

But as for as calling, a boyfriend should nomally be calling every day or several times a day, But then if you know he forgets why are you allowing it.
Call the night before and remind him, call him or text him early the next day to remind him again.

But if he is not willing to do something to help schedule, he is just not putting his share into the relationship

Take a break. Simmer down. Don't call or wait at all.

You're still mad. I don't blame you.

"I told him that I forgive him"

Then you did your part.
He screwed up. Now, that's in the past.

Let him prove he wants to be with you. He already knows that you do.

Next time, you may be busy.
Hopefully.