Wolfman's Gang War story arc is excellent, although Ordway's artwork tends to look ugly in comparison to Byrne's. Byrne's stories are mostly slight, self-contained, and feel like variations on silver age stories. Then there is the totally wrong story in which it's implied that Superman and Big Barda are hypnotized into making pornography. It seems strange that a story like this got allowed in a CCA-approved story, but the code was becoming increasingly ineffectual by 1987. The cleverest thing about it is the outs Byrne left for himself should someone compel him to say that the plot to make pornography was actually successful. Despite Mr. Miracle's shock at seeing the tape (it turns out Tom King didn't invent the idea of multiple panels in a row to show Darkseid's changing expression), he could argue that the tape is of th battle between Superman and Barda (although since she wins, Scott would be unlikely to be that horrified by it, since it's hardly lethal), and the scene in which Morrie Grossman is directing them, their clothes are still on, Grossman complains about their lack of emotional display, and Sleeze is concerned that Superman is resisting the hypnosis because he would never sleep with another man's wife.
Byrne may have been doing exactly what DC wanted for its flagship Superman relaunch, allowing the richer storytelling in the legacy-numbered title and one-offs in the flagship for more commercial reasons. These stories involve Superman encountering the Joker and Mr. Myxzptlk for the "first" (as in post-Crisis) time, and another story involving hypnosis, this time by Lex Luthor. The Action Comics double-header (the only issues of one of the three series that are presented consecutively) seems to imply that Superman and Mr. Miracle and Big Barda are aware of each other but have never met (which they had in pre-Crisis continuity).
The last story is particularly interesting. An alien in a burqa whom Superman apparently encountered previously in Qurac, DC's all-purpose fictitious Arab country, compels Superman through his dreams to help her people, though he tells her that if he had just asked he would be more inclined to help other than to just be rid of her. He dreams of Wonder Woman in that story, and she says, "We're the only two who can love each other," which is clearly contradicted by the Big Barda story, so it's strange that he would dream that and suggests that editorial, that is, Michael Carlin, wasn't paying that close attention. I should probably note here that New York City is presented as an expressly different place than Metropolis because Cat Grant needs to travel to New York City to deal with custody issues with the son, Adam, that she has with her ex-husband. It seems strange that this volume collects only two issues of Action Comics and four of The Adventures of Superman when this last issue doesn't seem to connect to anything (apart from Cat's custody hearings) except maybe a previous story I don't remember--as it's been a few years since I read the previous volumes [it was in volume 3]--but that should be clearer when I read volume six, as there may be internal reasons for doing so just as presenting the two issues of Action back to back was here. No other stories could take place while Superman was in the thrall of Sleeze.
One can only dream that this might have been better if Byrne had been assigned strictly the illustrating while Wolfman did all the writing. Still, the four issues of The Adventures of Superman that are collected here are well worth the read, and even though three tell a complete story, the events seem to occur in such a way, and over enough time that the other stories could easily have happened in the order presented. José Delgado and Perry "Jerry" White, Jr. are really interesting supporting characters. During the Invasion! story arc of 1989, Superman unmasks Gangbuster to find himself (although that's part of a plot by the alien alliance to get him off-planet during the invasion). This earlier story that introduces the Gangbuster shows that rather than being a big reveal of a character whose identity was unknown, Superman, was, in fact, a Gangbuster impostor, which just goes to show how different reading comic books singly (or in this case, as parts of an event) can lead you to see things in a completely different way than when you have the full context.