On my system, this produces a result where the vertical-axis labels jitter left and right by several pixels as the animation progresses:

Module[{tableOfExamples = 
   Table[Plot[E^(-Pi x^2), {x, -Pi, +Pi}, 
     PlotRange -> {Full, {-1.2, +1.2}}, ImageSize -> 270], 32]}, 
 Animate[tableOfExamples[[k]], {k, 1, Length[tableOfExamples], 1}]]

All 32 plots in the animated table are identical, so there's no difference among them to account for the jitter.

I see the jitter when I have magnification for the notebook set to 125% (setting in the lower-right corner of the notebook). When I change the magnification to 100% or 150%, I don't see any jitter.

I'm on Windows 10, and my screen resolution is 1920 x 1080.

The jitter on my screen is faster, but my screen-capture software under-sampled it.