If you wanted to lose the dangle, you could say ‘the expression constantly changes while watching’. You don’t need the ‘it’.
Although, I think the real problem is, that it says ‘the expression’ which is rather ambiguous - is it the expression of the subject of the painting, or of the viewer?
Whereas, if it said ‘her expression’ we would know who is who, and what is what, in the sentence.
‘Her expression constantly changes while watching it’. Would be pretty clear - in the context of already knowing the sentence is about ‘the Mona Lisa’.
Or a possibly better form might be:
‘The Mona Lisa - her expression constantly appears to change under the gaze of the viewer’.
And yes - as Cargill commented - you don’t ‘watch’ a painting - you view it or look at it - though, if you were trying to catch a moving expression, then I suppose you might be ‘watching’ - which means ‘observing closely, to see what happens next’.