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He has been tailing her for two weeks to find out what her favorite drink is, yet she is the only one who can get the targets room changed in the time they need? Two weeks seems like enough time to figure something else out.
Considering the situation, the plan they went with was probably the simplest/best one. She was emotionally traumatized, helpless, and loved her father. The whole point of the movie was that they didn't know she had the backbone to refuse.
Wasn't it difficult for Lisa to run in heels? She does trip at one point, but it was a little impractical and must have hurt a lot. It would have probably been much easier (and faster?) to run if she had taken them off. Granted, there's a Psycho for Hire running after her, but still. (... But then again, she wouldn't have the Broken Heelto stab him with, huh?)
This Troper is a drag queen, and trust me, it's not that hard to run in heels. Besides, would you want to run around an airport shoeless?
Its better to run in heels than potentianally cut or bruise your feet.
Rippner is a master hitman, as he tells Lisa on the flight. So why in the world does his master assassination plot involve firing a rocket at a hotel room from a boat, necessitating Rippner buying a ticket for a flight (probably there and back), arranging for a hitman to be posted outside an old man's house miles away for several hours, and depending on threats to a stranger in the middle of a long-haul flight to put the last and most important piece of the plot in place for him? Really? That was the best way to kill the guy?!
He never says anything along the lines of being a hitman (Lisa even poses this question to him, with him responding that he's a terrible shot). He's a "manager" - he just makes sure everything's in place so that the people who hired him can carry out THEIR hit. In all likelihood, he didn't come up with the master assassination plot at all.
The flight attendant thinks she just caught Lisa and Rippner having sex in the lavatory. Lisa is crying and obviously distressed, Rippner is sickeningly smug. Wouldn't that raise a few red flags? Granted, Lisa couldn't have told her the truth, but why didn't the flight attendant at least ask Lisa if she was okay?
How in the heck did Rippner beat Lisa home?
He had followed her for eight weeks, which presumably gave him time to memorize all possible routes to her house. Granted, she'd know her way better, but Lisa was in a panic at the time and was trying to make a phone call while driving a (stolen) car and evade the police and Rippner. It's still a bit of a stretch, but it is possible he could swing it.