Nursing records contain information on patients' treatment processes, which reflect the changes in patients' conditions and have legal effects. However, some of the written records of intensive care unit (ICU) nurses are incomplete according to our observations. This paper proposes an approach extracting structured nursing events from unstructured nursing records for detecting the missing items automatically. According to the PIO (problem, intervention, outcome) principle in the field of medical care, we propose event schemas for nursing records and annotate a Chinese nursing event extraction dataset (CNEED) on ICU nursing records. We find that several events may occur in a nursing record. Therefore, we present a multi-event extraction model for the nursing records. The experimental results demonstrate that our model achieves good results on CNEED and outperforms competitive methods on the multi-event argument attribution problem. By observing the results of automatic event extraction by our model, we detect missing items in the existing nursing records. This proves that our model can be used to help nurses check and improve the method of recording nursing processes.