Ho Yay: Some between the rancher and George the tractor manufacturer when they buddy up to fly to San Francisco. Parodied when everyone wakes up at the bar:
Rancher: (Walking up to George) Hey... didn't we fly up to the west coast together... Servo: (As George) No! Shh — we didn't... No, we didn't — WE DIDN'T!
Rooting for the Empire: Mike & the 'Bots are strangely sympathetic to the Enemy's propaganda broadcast after taking over the hero's radio station. Tom even starts humming the Soviet national anthem in an outbreak of Patriotic Fervor (after humming "The Star-Spangled Banner" during the hero's Deadline News moment.)
Hell, Mike and Crow start dancing to the Soviet anthem, such is their fervor.
The MST3K version of A Date with Your Family contains:
"Funny Aneurysm" Moment: Servo's "The Woody Allen Story!" joke when the title screen comes up is a lot more disturbing now that Allen's adopted daughter Dylan Farrow has spoken publicly about her memories of allegedly being molested at age seven.
Narrator: Do you begin to see now how a date with your family can be a truly special occasion? Mike:(as Narrator) Do you? DO YOU? Narrator: And why Brother and Sister looked forward to the evening? Mike:(as Narrator)WELL, DO YOU? BETTER SAY "YES", DAMMIT!
Squick: A reasonable reaction to the narrator explaining that the elder son should "help Mother to her chair like he would his best girl."
Mike: The less said about this, the better. Servo: Yeah.
Narrator: The women of this family seem to feel they owe it to the men of the family to look relaxed, rested, and attractive at dinnertime.
Values Dissonance: Remember, kids: Repress your emotions, smile constantly, never mention anything unpleasant (especially to your parents), never complain, women exist to serve the men of the family, fear the Dirty Commies, and let the government do whatever it likes in the name of beating the Red Menace! Basically, the only values the short and feature endorse that don't fall under this are "wash up before meals", "don't spend too long on the phone", and "help your parents with the dishes, especially if they made you dinner".