I may have to go back and re-evaluate my Lester Del Rey reading. Badge of Infamy is a stronger story than Police Your Planet, but it has similar weaknesses in its treatment of women. Again, here, we see an unreasonably angry woman who suddenly turns around at the end and "give[s] in completely". Thankfully, in this story, they don't live happily ever after. But the woman in the story plays a key role, and her actions make very little sense.
Gender issues aside, the setup is an interesting one. While the action is a little on the pulpy, side, the narrator is intriguing, and has some moments of uncertainty. He's a failure much of the time. Scientifically, well, there's a lot of handwaving, and it's enough to keep the plot moving, but it's not something you want to peer too far into.
I enjoyed the story, but it's largely for people really wanting to dig into the post-Golden Age middle period of SFF. It's not your best place to start with Del Rey. In fact, I'm starting to think maybe novels weren't his forte.