I only got stuck once. And that was only because I thought logically.
There was a situation where I hung off a ledge and I needed to half turnaround and jump off to a higher ledge behind me. Since I could not imagine this working with Earth's gravity, I didn't even try, I just looked up to that ledge and wondered how I might get there.
Once I got used to the idea that Faith defies stupid old Gravity, I never had this problem anymore. Although I'll agree that the construction site was challenging, but in a good way - for me.
I also managed a second walkthrough with very little killing involved. Some enemies you have to fight as part of the story and there was one instance where I needed to get up to a roof and I looked around a lot, the only way was climbing up a pipe. There were 5-6 policemen around and climbing the pipe always took way too long and I got killed, so I had to take them out.
But for the most part, you can really just run past them.