In the bar, Ensign Burke says that she's from Texas before she drinks a shot of bourbon. Actress Anne Winters is actually from Dallas, TX.
Admiral Ozawa is seen in command of the USS California. She had previously commanded the USS Olympia. Both are Leviathan-class cruisers.
Admiral Perry says The Orville will be escorted to Saavik III. Ted Danson, who plays Admiral Perry, was in Cheers with Kirstie Alley, who played Saavik in Star Trek II: The Wrath Of Khan. (Note: The name is spelt "Sabik" in the captions.)
When Isaac and Charly are using the laser drill, the main central panel closest to Charly shows a diagram of New York's Penn Station.
The vessel that absorbs the incoming fire from the Kaylon vessel while The Orville is locked in a tractor beam is the USS Constantino. The reference to "Constantino" is a lovingly placed Easter Egg put in by the VFX team's Brooke Noska that artistically illustrates the correct spelling of the Co-Producer's last name: Costantino. (Tom Costantino).