Dirty heads generally show analog noise on screen. Speckles of "snow" would be one example. Sometimes you'll get distortion of the image, but that has to be major dirt -- and possibly damage to the head, too.
The way to properly clean a head is to lightly drop some denatured or 70-90% isopropyl alcohol on a non-cotton swab, firmly but gently press the swab against the head, and slowly turn it one rotation. Do not press too hard, you don't want to damage the ferrite heads!!
Those "cleaning tapes" are largely crap, often causing damage to the heads.
If it makes you feel any better, I have a similar issue on a VCR here. Sometimes it randomly displays snow stripes on screen. Cleaning the heads properly doesn't work. I have a mylar cleaning tape that I run through the deck, and it somehow fixes it temporarily. A hour or two later, the problem is back. I have no explanation for it. You're the only other person to report this issue, and I've had it for about 6 years now. The problem, the mylar cleaning tape -- they sound identical.
Here's a simulated image of my annoying issue:
It's not a tracking error.
This deck is only used a few times per year, so I've not worried about it too much. Still an aggravation, though.
Too expensive to replace, too valuable to do without.