If a doctor sends screen grabs, taken by his smartphone, of different patients' confidential health files to other doctors for quick consultation, does that potentially violate any law? Could that be considered professional misconduct (and thus imperil his license to practice medicine)?
Health care providers in the US may send protected patient records to other health care providers for the purposes of treatment, either of the patient whose information it was or of a different patient (for instance, a doctor could send a chart of a different patient with a similar issue). This can be done without patient authorization, except for two cases: if the patient has requested more restrictions on use of their information and the provider agreed to those restrictions, and with psychotherapy notes. Source: HHS.
WhatsApp specifically does not appear to be compliant with HIPAA, which is the US medical privacy law. However, there are many similar systems that are compliant. The body of your question asks about taking a smartphone screenshot; with many secure messaging systems, this is perfectly acceptable, and the principle of a doctor consulting with another doctor about a patient is actually encouraged.
HIPAA violations do not by themselves result in any action against a medical license, nor can anyone besides the US government file suit based on a violation (everyone else is limited to complaining to the US government). Private lawsuits and (especially) license consequences are determined by state law, and are state- and situation-dependent. A doctor who calls a press conference to announce that this patient of his has HIV is more likely to face sanctions than a doctor whose violation was just not using a secure enough messaging client. HIPAA violations like this are not that uncommon, and generally result in at most a fine against the practice.