I too find it interesting that the theme changed every year except those two. But the graphics (or rather, the layout of the video footage used) did change a little during 1981. I noticed this recently when adding a few Countdown intros to an external hard drive and seeing that the layout of the February 1981 intro was different to the June 1981 one.
I think my favourite opening theme was the 1983 one, though the 1981/2 one is iconic.
I like how Countdown changed their introductions each year. At the time, it just signified a new year, I guess. But now, in hindsight, it helps differentiate each year as I enjoy the repeats of such a brilliant show from the 70s and 80s. I guess that's why, for me, it's a little confusing watching 1981 and 1982 episodes and seeing the same introduction. I don't instantly know which year it is.
My favourite introductions are from the early years. I love seeing the 70s introductions. So basic, but so classic! And so 70s! 1978 and 1979 are just so etched in my memory from back then.
In the 80s I like the earlier ones too, especially 1980 and 1981/82. As the decade progressed the introductions became more ... well, 80s. Fluorescent colours and electronic graphics were used. By 1987 though, in my opinion, they lost the plot, and tried to become cool all of a sudden. The introduction is so cringe-worthy when I sit through them now, which is not very often.