The Public Mooring is an Old/New World special building unlocked upon reaching 250 Artisans (or 600 Obreros). It doesn't need any road connection with other buildings and can be affected by both Harbourmaster's Office and Town Hall, being buffed by items which can reduce its maintenance cost, increase the island's attractiveness or the visitor chance. Income is directly proportional to island Attractiveness, being equal to 3.6 times your attractiveness or 3.6 times your visitors, if the second one is lower (the result is rounded down).
A second feature of Public Mooring is the chance to get "specialists": all those Trade Union, Harbourmaster's Office or Town Hall items who are real persons and not tools. Amount and rarity of these items depends on your overall city attractiveness, Culture Department's passive effect and Policy chosen at the Palace, completed cultural sets as well as any relevant items affecting the Public Mooring. Every 30 minutes the Public Mooring receives a visit, in which there is a chance to get one single specialist from a variable pool (according to different bonuses). The arrival of a new special visitor will be notified with a popup, as well as visually marked on the Public Mooring both with a light-blue arrow and a small circle on top of its window, showing a preview of the item.
Considering its maintenance cost, while Public Mooring income is directly proportional to island attractiveness it is profitable to build it with at least 112 in the Old World/Cape Trelawney, or at least 70 in the New World.
When an island attractiveness lowers, the income starts to decrease. However the rise of income due to growth of attractiveness applies only every 30 minutes, thanks to a mechanic called "visit": every 30 minutes a ship comes to the Public Mooring and balances visitors taking them in or out of the island, making them match the exact value of your attractiveness, according to Tendency. Tendency shows the variation of the Island attractiveness since the last visit, that is to say it is equal to the amount of visitors that will get in/out of the island with the next visit. Tendency being equal to 0 means that there have been no changes in attractiveness since the last visit.
When your attractiveness lowers your visitors remain the same, but will pay less (as island is less attractive) so in order to gain more you will have to raise the attractiveness again. As it was already said, your income will never exceed 3.6 times the amount of visitors or attractiveness (depending on which one is lower), so if your attractiveness surpasses visitors you will have to wait for the next visit in order to get more visitors, and thus the income you deserve.
A ship leaving a golden trail will be running around a purple circle: that gives quick information about the time left before the next visit arrives. Hovering the pointer on that, as well as other parts, will show additional information such as exact time left before next visit, chance of specialists and item modifiers.