When you are around people, they will sometimes talk about Ultor, which is the company from Saints Row 2. They will also say "Damn drones confiscated my feed dogs collection", which is the band from Saints Row.
The area "Mt. Vogel" of Mars is a reference to Dean Vogel, whom you were required to kill in the last mission of Saints Row 2. You also only get to enter it during the final mission just before the campaign is complete.