Luuc,
I, too, have done extra work for additional income. I know how crazy it can be!
As far as what skills it helps develop; I think there are many.
--First of all, many extras do not find out about their work until the night before or morning-of (I'm talking 12AM for work at 7AM, or getting a call at 6AM to be on set by 8AM). Such crazy scheduling is, I'm sure, reminiscent of the crazy, unpredictable hours that healthcare professionals endure. It also forces you to be able to quickly respond, get ready, become alert/awake/prepared for work within a very small window.
--Additionally, the hours that extras work may be horrendous. Ex: a 5AM call time, that works until 7PM or later. It basically depends on when the producer/director decides he has had enough. Or, a 5PM start time, with a 7AM end time (overnight). I believe that being able to work and stay alert and focused under such conditions may prepare you for the highly demanding schedules of physicians.
--As an extra, you are required to follow every set of directions exactly. One mess-up, and you'll be publicly humiliated and sent home (aka with no pay). This reinforces the skills of staying alert, and following all directions given by authoritative figures.
Clearly, the acting field is not related to the medical field. But I do believe that you can translate these skills into any profession (if translated quite well)
Just my two cents 🙂