You may be able to clean up the contacts on the display, not a definite fix but if you take the clocks to bits, gently ease the clips off the display, take it out, there is 2 foamy parts going from the display down to the actual main clock, a couple of blows and a little wipe along the bottom of these and it may improve things.
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If you are not confident enough tackling such a job yourself you could have a word with this guy... BMW E38 E39 X5 Instrument Cluster Pixel Repair Service | eBay
He does quite a few pixel repairs on E39's, X3's, X5's and other vehicles... The E46 dash is almost the same as an X3, I am sure that he can help. He can even do the repair while you wait.
I believe that his name is Chris.