Documents in the health domain are often annotated with semantic concepts (i.e., terms) from controlled vocabularies. As the volume of these documents gets large, the annotation work is increasingly done by algorithms. Compared to humans, automatic indexing algorithms are imperfect and may assign wrong terms to documents, which affect subsequent search tasks where queries contain these terms. In this work, we aim to understand the performance impact of using imperfectly assigned terms in Boolean semantic searches. We used MeSH terms and biomedical literature search as a case study. We implemented multiple automatic indexing algorithms on real-world Boolean queries that consist of MeSH terms, and found that (1) probabilistic logic can handle inaccurately assigned terms better than traditional Boolean logic, (2) query-level performance are mostly limited by lowest-performing terms in a query, and (3) mixing a small amount of human indexing with automatic indexing can regain excellent query-level performance. These findings provide important implications for future work on automatic indexing.