Bad optics or bad eyesight?

Ah, I think get it.

So if I compare several photos, I should see the "hot" pixels in all of them and in the same positions relative to the frame edges - but Capella will be in slightly different positions?

The camera is a Nytech ND5040 5 megapixel (from Lidl, where else) set on auto without flash. I'm just holding it up to the eyepiece and taking a 3 shot burst.

Hmm, time to read some of the astrophotography threads, I think.

That's your problem...it's just hand movement over the 3 second exposure...way too short for hot pixels to be an issue...but way enough to make the star images smear around instead of being points of light.
Anything over 1/60th sec exposure will start to show that shake....and any zoom will magnify it by the zoom amount as well.