Learning to communicate with code-generating AI models is an emerging skill for novice programmers. One recent pedagogical approach, Prompt Problems, allows students to practice solving computational tasks through natural language prompting. Little is known about the mistakes students make when interacting with AI or what strategies they use to recover. In a CS1 course, we studied attempts by more than 900 students to solve dialogue-based Prompt Problems. We analyzed student reflections, unsuccessful prompts, and reported debugging strategies. Compared to traditional coding tasks, students generally found prompting easier, more enjoyable, and better targeted at developing problem-solving skills. The most common mistakes related to omission of key details, suggesting both a failure to acknowledge their importance and over-reliance on AI to infer them. When prompts failed, students focused more on clarifying their intent and reflecting on the provided problem details, than on tracing generated code or examining test cases.