In the tutorial, jump on the van, then on the AC unit nearby, then onto the
fire escape.  Go to the top level and jump through the window to get a
congratulations message and some painkillers.

In act 1, chapter 2, you have to head back to the bombed door and rush three
men upstairs.  Kill them before the grenade is thrown at you, so you can pick
up the grenade.  Then, without opening the door, go back to the start of the
level and find a spot in a brick wall where several bricks are missing.  Throw
the grenade into the hole.  Now check your objectives -- it will say, "I had
declared a war against rats."  Go back to the door you didn't open before;
inside, the rats will be armed with guns.

In act 1, chapter 6, take a sharp left after jumping out the window.  The
window furthest down can be blown out.  Inside are some shotguns and posters
for "Solder of Fortune II."

In act 1, chapter 7, kill all seven of Gognitti's thugs, but don't take
Gognitti himself on.  Instead, go to the satellite dish and the ledge behind
it.  Do a running leap onto the ledge on the other side of the alley below.
Drop down into the area on the end.  Head through the door.  In the room
beyond, there are grenades, cocktails, and a picture of Dopefish wielding a
couple of pistols.

In act 3, chapter 4, right at the start, jump on some barrels, then the AC
unit, then the roof, and then blow the metal door open.  Get on the crate to
enter the room below.  Inside, get the sniper rifle and use the radio to get
a message from the Remedy team.

In act 3, chapter 5, get the blueprints and then, instead of going through the
door, shoot the painting on the left a few times.  It will fall and reveal a
button.  Push the button, and the couch will move and reveal a passageway.
Open the door at the end of the passageway.  Watch the TV for a Star Trek
parody, and then open the cabinet in the bedroom to see some...er, supplies.