[quote]When the ship is finished a day stop and it's time to depart, what happens if people are late getting back? Does it wait for them (and if so, how long)?
Depends on the circumstance. If an entire tour is delayed getting back (traffic, accident, incident), they will wait. There is plenty of time to recover at sea and arrivals at the next port of call are usually very early while guests are still asleep, so a slightly later arrival may cost the company some money in port taxes, but not necessarily in guest's enjoyment or well being(once that's affected it's time to star assessing how long to wait for a delayed tour).
Unaccompanied passangers here and there who are late do not fare as well. The ship will not wait for them. And with the increase in passenger volume per ship in the last decade of the industru, this kind of thing now happens pretty much every trip.
There have been exceptions, for instance a medical emergency with a proper phone call. But too many were the times were we'd be sailing off with a loud party going on aboard, and we'd see someone running out of a cab, shopping bags to the wind, screaming "STOP STOP!" to the excitement of those onboard who would wave back, but of no useful avail to the poor soul. A few were the times when I myself - a seasoned employee - would step out of a movie theater in wintery Norway, see that it was dark outside, and go into a panic only to realize it was three in the afternoon and dark already.
The ship's hotel will simply leave the poor souls' passports with the port agents and will not even be responsible for getting them back home (you sign things to that effect). People are adviced ahead of time about heavy traffic, transportation requirements, strikes, snafus, etc. in each port so they can plan accordingly if they decide to wander off by themselves. This also provides an opportunity for the travel staff to sell their tours, guaranteeing those who stick with a tour a safe and timely return, and if not possible, flights and accomodations in the unlikely event your tour has to be left behind (never happened in my years working for the ships).
Also, there ARE ports of call (less stable governments) where you are not allowed out unless with a tour. And finally, some ports where certain citizens will suddenly not be allowed in. Those are the saddest cases, because there are no refunds and the ship's company does not take responsibilty for any sudden decisions by port authorities not to allow certain people in. The only instance I remembered that happening was one week in St. Petersburg when the Russian authorities decided not to allow Colombians in. We had to deal with some pretty pissed off rich Colombians for the rest of the run.
Many times people who miss the boat (crew included) can catch a flight to the next port. Other times, guests simply get their asses back to the port of departure where they will await the ships arrival to get their belongings. Unlike airplanes, ships don't have tight luggage policies (for instance, the one where if you get off, so does your luggage), as they x-ray and metal detect everything that comes in and out, and they really can't go about trying to pack and locate all your belongings, so they just leave your passsport This might have changed since I last worked the ships.