The free-form portions of clinical notes are a significant source of information for research, but before they can be used, they must be de-identified to protect patients' privacy. De-identification efforts have focused on known identifier types (names, ages, dates, addresses, ID's, etc.). However, a note can contain residual "Demographic Traits" (DTs), unique enough to re-identify the patient when combined with other such facts. Here we examine whether any residual risks remain after removing these identifiers. After manually annotating over 140,000 words worth of medical notes, we found no remaining directly identifying information, and a low prevalence of demographic traits, such as marital status or housing type. We developed an annotation guide to the discovered Demographic Traits (DTs) and used it to label MIMIC-III and i2b2-2006 clinical notes as test sets. We then designed a "bootstrapped" active learning iterative process for identifying DTs: we tentatively labeled as positive all sentences in the DT-rich note sections, used these to train a binary classifier, manually corrected acute errors, and retrained the classifier. This train-and-correct process may be iterated. Our active learning process significantly improved the classifier's accuracy. Moreover, our BERT-based model outperformed non-neural models when trained on both tentatively labeled data and manually relabeled examples. To facilitate future research and benchmarking, we also produced and made publicly available our human annotated DT-tagged datasets. We conclude that directly identifying information is virtually non-existent in the multiple medical note types we investigated. Demographic traits are present in medical notes, but can be detected with high accuracy using a cost-effective human-in-the-loop active learning process, and redacted if desired.