My characters in Kingpin look like they are made out of some kind of liquid substance. The game also runs way too fast. And in the beginning, when your character is lying on the ground, one of the two guys suddenly appears several feet behind where he was previously standing and then suddenly he is back where he was originally standing. What can I do to fix these problems? They make the game unplayable for me.

If it work too fast try to disable CPU cores.
Ctrl+Alt+Delete ->find game EXE ->Set coligation (?).

I have the same, disable multicore
any ideas?

If you are referring to the wobbly effect on the character models apparently that is just normal for the game. Other games utilizing the Quake II engine have that same effect.

The wobbling effect was a trick for adding more life to the characters. Let them look less static by simulating motions on the face and the body.
Compared with today's games, it looks a bit archaic but in the time of Kingpin it was interesting...

read this
http://www.gog.com/forum/kingpin_life_of_crime/texture_wobble_on_characters/post3

Thanks. I've already seen this post. :)

But, I'm not convinced. Let's watch closely a Kingpin character with MDX viewer. For each animation, in addition to the main limbs movements, you can see clearly all the vertices slightly moving all the time, especially on the head. And, as the texture UVs are linked to the vertices, it explains the "wobbling" effect.

I think it was intentional from the developers. Otherwise, it would have been more simple to animate each limb as a block and only adjust overlapping vertices at the joints.

Was it a good idea? Not sure if people see it as a bug...

ah, so weapons are alive as well?

This is really due to the low precision floats used in the Quake engine. This also happens in the original Quake with the Darkplaces engine, if you enable interpolation(without the animations just look stuttery).