OK. In my iMovie11, playing the Project with the spacebar. If I use the spacebar to stop/pause play, the playhead doesn't move. I can then nudge it left or right by using the arrow keys. If you want to move the mouse, then hold down the ctrl key while you do it. With the ctrl key still pressed, left click and that brings up a menu where you can slit the clip.
If you are trying to cut from one clip to another at a very specific point, click on the cogwheel of the righthand clip and choose the Precision Editor.
Use the mouse to move the blue line to position the cut point where you want it.