Yep. They go wibbly when the character is tearing up, for example, as a direct representation of specular reflections off a wetter surface. Crystal ponies have hexagonal ones for crystal reasons.
 
All in all, so standard.

The number of eyeshines is pretty much a direct link to how cute they want you to see them as.
 
Notice that while a lot of ponies have two at least, Trixie only has one.
 
(Also, you are aware that eyeshine is literally an application of light so it’d logically change from scene to scene just like any other shading or highlight, right?)

Jeeze, so nitpicky

The number of spots change according to the nature of the scene. If she’s staring at something she wants, for example, they’re going to add more spots, and they’ll probably be slightly animated.

@when she felt her wings unfold  
I was thinking it might be oval because I perspective and not even an error. However they don’t necessarily change the shape much at angles, or it’s hard to tell because most of the eye is hidden when the head is turned.
 
Their eyes are generally more round but I’ve seen them oval-ish many times, doesn’t make it an error if it was intentional. (Just like the shape of their head changes spending on the mood trying to be set, which I guess is the deal with round/oval eye changes in the fillies)
 
All in all I see no errors here just standard animation techniques.

@Techy Pony  
The “error” one is in perspective too, on the side of her head, right? Ellipses are kinda what circles do at an angle.
 
More context needed, I think. The roundness is another cuteness cue for the younger characters, and I dare say there’ve been face-forward shots of foals with two circular eye shapes. That said even >>160708 (merged) doesn’t do it, and that’s one with the cuteness dial turned up to 11 deliberately.

Just the spots then?

@Background Pony  
That’s not an error, it’s an animation technique they use often.

number of white reflective spots
 
boooo

I don’t get it…

@VoltraTheLively  
No, mares/fillies are usually segmented. I think it’s that the error is her eyes are oval when they should be more round. (Fillies = rounds, mares = oval)

It’s used as a visual shorthand for cute.
 
You are now imagining filly Fluttershy with 6 or 7 eyeshines, each shaped like a butterfly or a rabbit or something.

One’s a gradient and the other is segmented?

Nope.