Jittering= picture jumping up and down, yes?
After a monitor's been on for a while, the circuits will get hot. After a few years, some solder points will loosen up when the temperature rises and you get some faults that are only detectable after the monitor's been on for a while.
If you open the monitor, you'll notice several coils around the CRT itself. They're the ones that control the electron beam that hits the phosphor. A pulse is being sent through them that's synced up to the RGB signal and it creates a varying magnetic field inside the tube that moves the electron beam around on the screen.
If those circuits are getting unstable, you'll notice a jittering image. If one of them stops working, you'll get either a vertical or a horizontal white stripe on your monitor. You'll find those circuits by simply following the cables going from the coils and to the circuit board. Each of them should be a transistor-circuit. Usually hooked up to the heating sink.
I suggest you leave your monitor on and hit the components with something made of plastic (like the handle of a screwdriver) when the image starts to jitter. If you notice it getting better or worse, you can try resolder the contact points on that component. If you're lucky, you'll find the component that way and the problem's solved.
The time it takes for the capacitors to discharge completely depends on the model. There's usually a big one that's a part of the AC/DC converter around where the mains cable is connected to the circuit board. That's the only one that's given me a jolt when I've fiddled inside monitors and TVs.
Use a multimeter set to measure current and then put the pins on the capacitor if you want to discharge it or see if there's any charge.