mod_tile renders OpenStreetMap without some water

What went wrong?

Part of your toolchain is likely not handling OSM multipolygon relations well, or not at all. Many big waterways, even if they don't have interior rings (think donut shape polyon), still use the multipolygon relation as a means to manage very large geometries.

Unfortunately, even though multipolygon relations fullfill a clear role in OSM, and have been around for a very long time now, there are still tools out there that don't handle them due to the complexity of processing and the developers unwilling to invest the effort.

I personally think that any tool incapable of handling OSM multipolygon relations is of no use nowadays with the amount of MP relations created in the database.

Anyway, you may be missing any donut shaped buildings and other stuff as well, e.g. think of a building with an interior courtyard, so be aware this is likely not an issue related to waterbodies alone, but generic to your import and toolchain.