Well, the magnetic fields around the speakers are probably somewhat irregularly-shaped. You could do some experimenting, if you were so inclined.

Can't speak to the DVD-R thing, particularly, except to note that I'm a huge fan of The Wire. My usual advice is to clean the disc and power-cycle the electronics, but you've probably already done those things.

Gremlins.

The earth's magnetic field varys by direction. This is how compasses work. The same magnetism that moves the needle is at work moving the electron beam across the monitor at a very high rate. The electronics that control it are very sensitive and calibrate themselves to the conditions when you turn on the monitor. By rotating it you throw them out of whack. Try rotating the monitor, turning it off, waiting a few moments, and then turning it back on again. It should show a clear picture with no distortion.

The FBI's secret listening devices.

Specklet has it. Or, you know, maybe Rhomboid is onto something as well, but that's no fun at all.

I thought Rhomboid's explanation was fun.

Rhomboid's mostly right. In CRT factories, final settings are always made with the monitors facing east, so that they come out uniform. Repair benches are also set up so that the monitors can be recalibrated while facing east.

Rotating your monitor shouldn't cause dramatic changes in display quality because of the earth's magnetic fields. It's more likely to be caused by something manmade near by, such as an electrical transformer outside one window. Unshielded speakers can also cause distortion, but pretty nearly any desktop speakers sold these days are magnetically shielded so they shouldn't be the cause.

...on the other hand, the subwoofer in three- and five-piece speaker sets is usually not shielded because it's expected to sit on the floor. Make sure it's at least two feet away from your monitor.

Get a magnetic compass. Go outside, determine which way north is. Go back to desk, remove monitor, put compass where monitor is.

If the north needle of the compass isn't pointing north, something is convincing it otherwise. Move items around and you'll find out what is doing what.

If the compass is pointing north, move speakers, see if the needle moves dramatically. (This is a check, just in case...) The reason to use a co
Otherwise, there's something producing a noticeable magnetic field instead of just moving things around is that if you magnetize the shadow mask in the monitor enough, you'll never get rid of the color fringes. [1]

Magnetic field drop off with the cube root of the distance, so proximity is a big issue, and lack thereof is a fast fix. A speaker at 6" might cause problems, at 2', it'll be fine.

1) Large rare-earth magnets, like N40 or better NdFeB magnets, are power enough to bend the shadow mask in a monitor if they get close enough to the screen. This is"game over" for a useful monitor.