A simple test, that worked very well for me, was testing my reading speed (I know it is only a weak indicator for mental acuity, but it is easy and fast to test).
Under perfect conditions (well rested, optimal nutrition, completely silent room, no visual distractions, after mediation and a good cup of green tea) I am able to read about 800 WPM (which is not to bad) of the kind of text I usually need to read with good retention. For me this declines rapidly to less than 200 WPM (which is quite bad for a "knowledge worker") with sleep deprivation and/or a noisy environment, even though I believe I am doing fine.
That being said, even though I would say that doctors are handicapped "mental performance" is handicapped by their working conditions, I fully agree that it is better for patient safety to not hand off a patient to a new doctor say every 8 or 12 hours due to the amount implicit knowledge that a doctor gathers during a >24h time period about his patients that can't be transferred in a handoff.
Software Developers, imagine what a screw up it would be if you'd have to hand off your code every 8h to another developer, who'd have to continue right were you left... add to this not having a version control system, spotty test coverage and highly ambiguous specifications