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Without further ado, here is what I would change about Black Adam.

Theme

I like to start with the theme of the movie. In Black Adam (BA), I'm not entirely clear what the theme they were going for was.

But let's take one of the scenes from the movie, where BA faces off with Hawk Man (HM). HM tells BA, "Heroes don't kill people", and BA responds "Well I do."

In multiple different places they talk about what's right and what's wrong. Heroes and Villains. It's easy to tell who's bad and who's good when you're the one drawing lines. When you've seen so many futures as I have you cease to believe in absolutes.

One of the biggest BA marketing push is BA's version of justice. He's bad ass. He kills people.

Based on all this, I think a good theme would be: "Justice is not black and white"

The movie would then examine the concepts of Justice, due process and when is it okay to bypass due process for the greater good.

This can be done by creating a contrast between HM and BA, since both of them embody the different ideologies.

What would make the movie good IMHO is if we never really come to a solid answer, rather show how both approaches have significant flaws.

If you wait for due process, you end up with injustice prevailing and people suffering. 

If you shortcut and "kill them all, and let God sort them out", then you end up hurting people who don't deserve it.

This conflict would be best embodied by having a character who turns out to be a reluctant Judas. Let's see how we can do that by examining the characters in the movie, and assigning each one a role in the script.

Characters

Let's look at the characters from their thematic roles perspective

Black Adam

He embodies the alternative view on justice. In order to help people you have to have some darkness in you. Sometimes you have to make the unpopular choices.

Hawk Man

He embodies the Idealistic super hero. The one whose goal is to keep the peace; to maintain due process; to ensure traditional justice is carried out.

Adriana and Son

I'm going to ignore the son character, because he serves the same thematic purpose as Adraina. The only thing he adds is a connection between BA's past and the present. He serves as a reminder to BA of his own son. Although this doesn't come out very well in the script.

She represents the oppressed people, who suffered at the hands of the Villains. She wants justice, but lacks the power and resources to actually make it happen

Ishmael

He represents the evil in man. Him and Intergang serve the same purpose. They oppress the of the people of Kahndaq; mistreat them; and take away their freedom.

I think I'm going to stop here, as these characters are the only one necessary to drive forward the plot in its bare essence.