Here is my top finds in the Just Cause demo. It is first a description of the bug then a video showing it. They were all found during a single week. The reason the clips aren´t longer than 30 second is that I did not have a full copy of fraps at the time.
Just cause demo found here

Title:
Player invisable in cut scene
Description of bug:
The player doesn´t show up in the cut scene. But all enemies do.
How to reproduce the bug:
After starting the revolution to take out the second mark run to the first blockade before the cut scene starts
Video of the bug:


Title:
Unclimbable ladder
Description of bug:
A ladder is placed so it don´t lead anywhere and when trying to climb it You fall down.
How to reproduce the bug:
When trying to get to the third mark instead of going up the stairs follow the building to your left and when you see two ladders, try to climb the one that is against the wall.
Video of the bug:


Title:
Multi jump
Description of bug:
When jumping and switching weapons you make another jump in midair
How to reproduce the bug:
When jumping switch weapon directly and You will make a new jump in midair, but it seams this do not work with every weapon, the ones I succeded to do multijump was switching "Harker 357 Sawback" and "Aviv Panthera"
Video of the bug:


Title:
No collision with rotor blades
Description of bug:
Nothing happens when the rotor blades collides with the boat or anything else
How to reproduce the bug:
Get the helicopter and try hitting things with the rotor blades
Video of the bug:

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