We took the car seat on domestic flights and DS HATES it on the plane. Non-stop screaming unless we take him out, so CARES (harness type for planes) it is for us. Also, convertibles are huge - there will be no space between the car seat and the seat in front of it, and DS kept kicking the person in front of us, which will lead to problems (we took him out of the car seat!). My niece did the same thing and actually got yelled at by the passenger ahead of her (she was 2 then).
He now is not interested in watching TV much, he just started recently, so DVD players are not an option (I do believe though that next year it will be heaven to have a DVD player with us - 3 year olds are a different story!). So I entertain him non-stop. Games, peekaboo, new toys (he couldn't care less, they all end up on the floor within 2 minutes or less), looking through books and the SkyMall magazines, going to the bathroom (he loves washing his hands), bringing "junk food" (waffles, chips, chocolate - all the stuff that is usually reserved for special days and consumed very little) and vitamin water - stuff he likes. It is super stressful to keep him from freaking out (he hates being restrained in a seat on a plane).
At the airport, since I travel without DH mostly, I check my stuff. I pay for it, otherwise logistics are impossible. I bring a travel stroller, a backpack and a small lunch bag (insulated, for yogurt and milk which he loves). That way I can maneuver and won't get tired out too much. Be prepared for security - some airports are stricter than others. in Denver I always get pulled aside (4 out of 4 times), have to open his water and milk bottle, it gets tested for fumes or vapors, then you get it back. You also have to collapse the stroller and put it on the belt for the xray, which is a pain since nobody helps (I just did it last week, visibly pregnant, and they couldn't care less, really, do not expect help, and if you ask people, they usually don't help either, in my experience). It's such a pain - they also always insist that DS takes off his shoes, which leads to a minor tantrum (he neither wants to let go of shoes nor strollers, ha). Security is one of the worst parts for me of traveling (btw, only Denver and Chicago put up such procedures for me, Detroit, San Francisco and Frankfurt were totally different!).
Oh and yes, United Airlines wouldn't let me keep DS in the MaiTei during takeoff or landing nor have him at least somewhat buckled in my seatbelt (he was a lap baby). I just waited til we were on the runway, stuck him back under my seatbelt (better a little than none, and better broken leg bones then a baby flying around in a plane) and nursed him, put the blanket over us so nobody knew.
And for the strapped in - American Airlines was ok with not buckling him in til we reached the runway. Frontier Arilines wouldn't leave the gate without him being buckled. They also waited a full 9 minutes until he stopped screaming before they left the gate. I think they wanted to kick us off if he didn't stop. And I have gotten grief from some flight attendants, a Delta one told us to better drug our kid cause something is wrong with him for screaming like this... Others are nicer and offer cookies or make silly faces. I never had trouble with male flight attendants, interestingly. Passengers are a whole different story. They glare, roll their eyes and make stupid comments - mostly business travelers, single people, younger people. Older people or other parents have always been sympathetic and helpful with us (and mind you, DS's worst crying fit last 15 minutes maybe). Just last week when we sat down the lady right next to us rolled her eyes (right in my face) when she learned we were sitting next to her. Also on Monday on our way back DS touched once the LCD screen to point out our car in a commercial that was running (he seriously touched the friggin screen for the first time) - the woman in the seat in front of him then hit him with her rolled up People magazine. I didn't know what to do, but she didn't get him, only his fingertips, and I was too scared to say something, as I thought I will prolly get kicked off the plane, not her. On a recent flight from Europe to the US a couple in front of me complained non-stop about that "stupid cry-baby" on the plane, a circa 8 months old boy. Oh and how they hated those evil 5/6 year olds who dared to run to the bathroom. Oh my. I always wish I could tell these people to zip it and put up with it or fly private jets...