How to determine if an aircraft type is currently under investigation?
All aircraft are constantly under investigation. Service bulletins and airworthiness directives are issued for every certified plane and engine. These are optional and mandatory checks and maintenance to be done in additional to the normally scheduled maintenance. Every accident and important incident is investigated by the NTSB, with a public report available online.

There is a period of time before an airworthiness directive is made final that might be considered an investigative phase, but information on this is generally not publicly available. One notable example pertains to the rudder controls on the Airbus A-300.