I'm not happy to be giving Flip-Flop such a low rating, because frankly, episodes that get clever with non-linearity and time shenanigans are one of my chiefest delights in Doctor Who. While I can commend Flip-Flop for its clever construction and originality, I simply cannot say that this was an episode I enjoyed.
I shall get the most obvious issue out of the way first: the Slithergee. They seem like obvious bigoted caricatures, striking out at refugees and people with disabilities at once. One could certainly argue that they're meant to be a criticism of people who use their positions as minorities to excuse themselves of the blame for the harm they cause to others, but for that argument to hold, the episode would have had to delve deeper into the characters of individual Slithergee, which it does not. Plus, if you want to see that angle done well, look at Miriam in Jubilee. In comparison, the Slithergee struggle to come off as anything but a blatantly bigoted inclusion to this story.
The Slithergee are not alone in coming off as caricatures in this story. Every single character in Flip-Flop, aside from the Doctor and Mel, seem like cardboard cutouts of characters. President Bailey in particular strikes me as a totally motiveless character, and the dialogue in the scene where she sleeps with her secretary is almost comically unrealistic. The rest of the characters similarly seem to be easily categorized by one word personality traits – dumb, violent, greedy – that leads the entire plot to feel frustratingly farcical.
There are certainly some strong elements in this story; in particular, it's quite fun to realize how the pieces of the story fit together, and realize how earlier details given about the events of the day came to pass. I am, after all, enchanted by story structures like this.
However, the long and short of it is that stories need substance, not just structure, and what little substance there is to be found in this story is lackluster at best, and offensive at worst.
But hey, at least there was a Mind Peeler! When the Eighth Doctor mentioned it in Caerdroia, I thought it was a joke. Shows me, eh?