During the banquet scene, Captain Mercer says "we all do better when we all do better." This is a phrase that was famously used by Minnesota Senator Paul Wellstone.
The weapons the guards/soldiers carry are FN P-90s (FN stands for Fabrique Nationale and were designed and build in Belgium). Futuristic looking but they have been in production since 1991. These type of weapons were also used on the TV show Stargate SG-1 (1997).
Cpt. Mercer at the banquet says, "... we become a way for the universe to know itself." That is a variation on one of Carl Sagan's better known lines.
At the beginning of the scene where the crew of the Orville is shown the communications array control center, a city landscape is shown. There is a slightly pyramidal tower to the left of the array (from within the control center, it is to the right of the array). This building is an exact replica of the Landmark Tower in Yokohama, Japan.