Take a cab/Uber to the airport
Nothing starts off a couple's vacation better than a traffic jam peppered with comments like, "I TOLD you to take the toll road. Why are you so cheap?" Knowing that a driver is arriving at a set time holds you both accountable to a strict deadline; and more importantly, you have a third party to blame when you're late.
Don't watch each other pack
You'll go nuts trying to figure out why someone packs the way they do, so unless your partner is planning to smuggle black tar heroin, don't concern yourself with what's in his or her suitcase.
Check bags. Or don't. But never mix the two.
Either you both are carrying your bags on the plane, or you're both waiting at the baggage carousel. That way, you're in the same boat and there's no passive-aggressive resentment should a delayed bag eat into your beach time. If you're dating someone who has an irrational hatred of roller bags, this is an easy compromise.