I finally got around to listening to the first one, "Infamy of the Zaross", yesterday. No, I didn't pounce on them immediately. I couldn't wait for the first series - I downloaded the return of the Tenth Doctor as soon as it became available (which was the night before the official release date in the US, due to time zones) and listened to the first episode right away. This was the second series, and this was Rose, so there was no rush.
The tl;dr (posted at the beginning of the review, like it should be, rather than at the end) is that "Infamy of the Zaross" isn't worth it.
It certainly isn't the worst DW story ever, and I wouldn't categorize it as bad, but it's not good. Maybe poor. The main concept of the story, of the aliens invading because they're filming a TV show in which the army invades different planets, is clever and interesting, but the episode fails to capitalize on the opportunity to make interesting observations on reality shows or on the concept of an advanced race treating humans like cattle, and instead focuses on the easiest, most obvious message of "how dare you kill people for entertainment, fame, and fortune".
The form of the story is formulaic and predictable. The aliens invade Norwich, where Jackie happens to be visiting a friend, Marge, and her daughter, Jess. Marge and Jess are only given a few lines of interaction to establish their conflict with each other - Marge thinks Jess, who wants to become an actress, is useless, especially compared to her older sister who is a student at Cambridge - and my immediate thought was, "Oh, now she's going to do something to benefit the aliens, in the mistaken belief that it's going to prove to her mother that she's worth something." (Spoiler: I was right.) Jackie calls Rose and the Doctor, and they figure out that this is a TV show. The Doctor attempts to point out that it's immoral to kill people for money and ratings, but neither the filmmaker race (I don't remember their name) nor the actor race, the Zaross, are buying it, as they're after fame, money, and ratings. The filmmakers, in turn, offer the Doctor and Rose a place on their show, promising money and fame, which of course they turn down. Then, as the two races try to hunt down and kill them, the Doctor learns that the filmmakers are double-crossing the Zaross, and so he tells the Zaross, and the Zaross obliterate the filmmakers.
In the middle of all that, during the negotiations between the Doctor and the filmmakers, Jess suggests to the filmmakers that, since what they're after is ratings, they should shake up their formula of having the army invade a planet, and instead, film an episode of the army hunting down the people trying to stop their show. The episode ends with Rose talking with Jess, to tell her that she's important and that she shouldn't put up with her mother's disparagement. Jess responds that she was happy to die up there, because at least she'd become famous and she'd show the world how good she was, that that was better than living and being useless. So, Rose goes out and tells Marge to start valuing her daughter and tells Jess that if her mother ever puts her down again, to put her foot down about it and leave home.
There really wasn't much for the audience to figure out. The pre-credits teaser showed in no uncertain terms that someone was filming a TV show, so, as the invasion transpired, it was rather obvious that it was a reality show. Events after that revelation were pretty standard. Marge and Jess were entirely unnecessary for the story except to give Rose something to soapbox about, which, admittedly, is a pretty good characterization of Rose.
Beyond the plot itself, the story was just not inspiring. I remember when the first series of the TDAs came out and I sat down to listen to the first one, "Technophobia". It was a decent episode, but the energy of the action and the dialogue immediately sucked me back into the Tenth Doctor era. That didn't happen with "Infamy of the Zaross". The episode plodded along, and the dialogue served to tell the story but not much else.
Performance-wise, DT did a good job, though not as well as he did during the first series, but perhaps that might be because he had less to work with. BP didn't bother to get into character at all; she sounded like a generic thirty-something Brit, not a nineteen-year-old London chav. In fact, I couldn't actually tell the difference between Rose, Marge, and Jess, and had to rely on what was being said to figure out who was speaking. Nicholas Briggs did a better job playing Rose in the Ninth Doctor Chronicles. I am, however, becoming more and more impressed with Camille Coduri with every new audio she's featured in - she was stellar in the Ninth Doctor Chronicles' "Retail Therapy" - and am starting to look forward to the upcoming Short Trips about the Metacrisis Doctor that she's narrating, simply because I'd like to hear more of Jackie.
After this disappointing effort, I'm hoping that the other two stories in TDA Series 2 are better. The last one was written by Mark Fitton, who wrote "Technophobia", so I'm optimistic.