What should I think about when flying in the third trimester?

Ask your OB !! I tell my patients if they have no problems they can fly up till 32 weeks gestation and not after that.
Hydration, activity. The single greatest risk for flying in the thrid trimester is development of a blood clot in the leg that can travel to the lung. The best way to avoid this is getting up every 2 hours to get the blood pumping out of the calves. Pointing and flexing the feet can do the same thing. Another risk can be going into labor. Drinking lots of fluids can decrease this and also prevent constipation.