I think Jamie might have the best luck of any companion I have ever seen based on this episode.
Yes, the mysterious people behind Chameleon Tours took Inspector Crossland…somewhere, but by now, the Doctor has gotten most of the regular people in the airport on board to help except the officious commandant. So, when the Doctor, Jamie, and new friend Samantha barely survive a slow moving laser (because the bad guys use James Bond death traps) thanks to a compact mirror that of course Samantha had in her handbag, it may be time to check out the first aid station (some nurse won’t let them in), and then to lure her out so the Doctor can look around inside. If he’d just turned around when he briefly opened a door and saw the unconscious nurse, he might have made some real progress.
But by now, people are checking where those Chameleon flights land, and no one gets off. The Doctor figures he can check the plane when it returns. Also, he can have Jamie and Samantha keep an eye on that kiosk.
Has he noticed yet that Samantha tends to do her own thing anyway? Jamie has. So, when she buys a ticket for a Chameleon flight to follow her missing brother, Jamie goes in for a kiss…and swipes her ticket.
He still doesn’t have a passport…
Regardless, he gets on the plane, and a Royal Air Force fighter follows them.
But those Chameleon jerks knock out the airman, and the Doctor back at Gatwick sees the plane go down on the radar, but then the Chameleon flight appears to do the same thing. The Doctor suggests it’s going up instead of down. The commandant scoffs. But the plane is going up to a space ship of some kind.
So, why is Jamie so lucky?
Well, when the mystery beam makes the other passengers disappear, possibly by shrinking them down, Jamie wasn’t there. He got airsick and ran off somewhere, so he might be fine since he wasn’t in his seat.
This is the sort of thing that only the Second Doctor’s adventures seem to have, and it’s also why I love ’em so.