That's what Gergo explained. The right-floated video is pushing down the left-floated images, because floated images cannot be higher in a page than previously floated images.
You can fix it by altering the location of the video (move it down, perhaps below the second image). But then there are various problems depending on screen/window width (e.g. "sandwiching" at narrow widths), which I don't have time to determine an optimum solution for.

On Fri, Aug 7, 2015 at 12:12 AM, Pine W <wiki.pine@gmail.com> wrote:
More specifically, my issue is that the two left-aligned thumbnail images, [[File:Mukudori 05z4384cs.jpg|left|200px|thumb|Adult male (left) and female]] and [[File:Mukudori 0406214s.jpg|thumb|left|Fledglings]], are being displaced downwards from where they should be. The first should be in the "Description" section, and the second should be "In popular culture" section.

Pine


On Fri, Aug 7, 2015 at 12:00 AM, Gergo Tisza <gtisza@wikimedia.org> wrote:
On Thu, Aug 6, 2015 at 11:07 PM, Pine W <wiki.pine@gmail.com> wrote:
This is the second article recently in which I've encountered unexpected behavior when trying to align images.

https://en.wikipedia.org/wiki/White-cheeked_starling

Am I missing something, or is there a bug that's resulting in images being misplaced?

This would be easier to answer if you explained what the unexpected behavior is :) 
If you are referring to the vertical positioning of the image, it is pushed down by the previous (right-floated) image which in turn is being pushed down by the infobox. CSS 2.1 9.5.1 has the exact (rather complex) ruleset for positioning floats, the relevant part here is that a float can never be higher than any preceding float, even if they are floated in different directions.

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