Check out the full Hitman: Absolution Walkthrough for hints on working through the game.
There's a short sequence in which Kane (from the franchise Kane & Lynch) starts a bar fight in the Hope first take portion, in Welcome to Hope. Shutting off the electrical switch past the swinging double doors activates the scene. Another opportunity to see Kane comes when you revisit Hope: "Skurky's Law," in the "Hidden Cells" part. Follow the path the guard takes that leads down some stairs and you'll arrive at a vent. Follow the vent halfway to its opposite end and you'll notice the "peek" option, which allows you to watch Kane writing a letter to Jenny (like he did in Kane & Lynch).
During the mission Birdie's Gift, you'll be able to find Lynch testing a shotgun on the right side of the shooting range. If you shoot one of the gnomes off to the right, Lynch will get kicked out of the gun shop and you can take his shotgun.