I can see it's there - have a go using "res/tileset.png" instead of "/res/tileset.png"...
<edit>Ok, was just checking. Looks like it may be a slick issue then. Can you read the input stream yourself using that piece of code (instead of passing it off to Slick)?
Locally, no. However, I can do a "new Image("res/tileset.png"); and it will work, locally.
Fizzy Bricks (the physics game Kevin Glass wrote in two evenings to introduce the Fizzy overlay of box2d), initializes it's resources this way, in the applet: new Image("res/whatevs.png"); and it works in the applet as well.
Jar structure looks the same to me, of the two.