My DH and I also used to get sick on our vacations; I believe it is exposure to all the germs on the airplane (from the people with you and the poeple before you on the plane).
What I did for our honeymoon (2 wonderful weeks at WDW) was start taking a Vitamin C and a Zinc tablet each day for about a week before we left (building up our immune system), then continues with the extra C and Zinc while we were there. This was in addition to our normal multi vitamins we take every day.
We did not get sick at all that entire trip! Also, we did this again in January (10 days at WDW), and had the same results - didn't get sick!
Also, for the very dry air on the planes. I have chronic sinus problems that get much worse with very dry air. I usually have lots of problems on the plane, and have in the past wet down a napkin and breathed through it to help keep my sinus moist (hadn't thought about using he saline spray).
However, I just recently got a small personal air purifier from Sharper Image. It hangs around your neck like a small pair of binoculars, and it directs a flow of purified air to your nose and mouth. This would help with the germ things. But the REAL reason I got it is there is a filter that the air flows through that you can moisten with water, and now your purified air is ALSO humidified!
I haven't used this on a plane yet, but I will next weekend when we fly to Baltimore.
I got mine for about $20, using the Auction part of the Sharper Image website - I think they normally sell for $60 (which was too much for me to pay).
My two cents!