Back atDuring the questioning of Alec Forrester.

Nothing wrong with them but* for beingit though it was riddled with swear words.

But Steine merely waved him on, partly because he had no recollection whatsoever of them, and partly because his mind had turned to** other matters.

You, an actor, didn’t even show up at the theatre to take part in the play...A man who is able to behave with such sheer unprofessionalism, what else is he capable of?

Then, he and Brunswick argues over releasing Forrester.

Brunswick argumentes that the suspect beis kept at least another day in custody.

Steine is adamant that Forrester cannot be the culprit on the ground thatas no one has ever seen him with a gun.

Inspector Steine watches in pain as Sergeant Brunswick quotes a number of passages from witnesses’ statements.

"witness statements" is better to use here, i think

To Brunswick’s credit, he did ask Steine for permission to read out these sensitive passages out loud.

Now, Steine takes the lead, seeking to corner Forrester.

It might be argued that Steine’s strategy is not sound, but then he just wants to get this interview over with; h. He has far more important matters to deal with.

So, his attack goes something like this: “We have threats, a motive and an opportunity.

You do not need a comma after "So" in this sentence

You, an actor, didn’t even show up at the theatre to take part in the play...A man who is able to stoop to such sheer unprofessionalism, what else is he capable of?

It looks like you were missing a verb in your original sentence. "to stoop" means: "lower one's moral standards so far as to do something reprehensible." (definition taken from Google)

Especially, if this man has a grudge, an opportunity and a gun?” Steine lets his words sink in.

You do not need a comma after "especially"

Steine has hardlyJust as Steine starteds to believe he has finally nailed it, when Forrester spoils everything, saying, “But...I don’t have a gun.” Steine gives up in annoyance.

I rewrote the sentence to be in present tense and made some stylistic changes to make the sentence easier to read

Then, he and Brunswick argues over releasing Forrester.

"to argue" takes a plural subject here (he and Brunswick) so you need to conjugate it as "argue"

Brunswick argumentes that the suspect should be kept at least another day in custody.

"arguments" isn't a verb, it's the plural form of the noun "argument". the verb form is "to argue"

Steine is adamant that Forrester cannot be the culprit on the grounds that no one has ever seen him with a gun.

"on the grounds" is usually spelled with the plural. most English speakers say it and hear it used with the plural, so that's why I changed it.

*which is better "save (for)" or "but for" (assuming they're both right)?

They are both right, I think either could be used. I think I usually see and use "save for"

**can I say “drifted on to other matters” as well?

I think you can say that, yes. I haven't seen that exact phrase before but it makes sense to me when I read it