Well, I never expected to "see" wind since it's invisible. But the effects of it should be seen. It was just inconsistent.
But that's the point; the effect or the idea of "wind" is present in pretty much every sequence, either visibly or via auditory effect.
In the third act at Alcatraz you can see her hair being blown back as she rises (before Callisto jumps her). But later, when Logan told her to go so he could confront Jean, she just took off like Superman: her eyes stayed brown and there was not even a hint of breeze effect on her or Logan.
Actually, when Logan tells her to go, you can hear what might well be a wind effect as she takes off and her cape blows, and her hair moves as well, in what might well be wind. Actually, everyone's hair is blowing due to what Phoenix is doing, including Magneto's.
Its hard to say in terms of the sound effect, because Phoenix is also kicking up wind and her powers have their own "fiery wind" effect.
But listen to the sound during the shot of Storm taking off and look how it matches up visually; I don't think it can be discounted as Jean's "power effect" outright. Even if it was, you could argue Jean's power simply drowns out any wind Storm may have mustered.
Earlier in the battle, the angle is such that you can't really see her eyes well enough to tell whether they're supposed to be whited out when she takes off before Callisto attacks her, or if she's just looking up as she starts to rise into the air. She's summoning lightning and thunder as she continues to rise, and her eyes are opaque when Callisto does attack her, but that follows, because she's making a storm at that point.
This detail was also missed in the Danger Room sequence: she was channeling her powers--even transporting Logan with her in one instance--and yet her eyes never went white. If they have to go white when she clears fog at Alkali Lake, when she went airborne at Jean Grey's home, or summons dozens of tornadoes in X2, consistency would suggest the same for the above instances
I don't think it was missed. I think it was very much intentional.
The white eyes have always been used for dramatic effect. For when Storm is making storms.
Storm's eyes, during the franchise, tend to only white out when something very dramatic regarding her storm creation is happening. There were less dramatic moments for her as well when she used her powers in the film, and her eyes didn't white out during these moments.
Also, the film shows that Storm doesn't necessarily even have to concentrate anymore in order for her emotions to change the weather. The scene where she's creating dark clouds while lost in thought, for instance. She's got her eyes open, and they're not white.
The overall inference in X3 is that her powers are growing, and she requires less effort in general to use them. More to the point, she only has to do so to create storms. Flight looks pretty effortless and routine for her by comparison.
We only see her eyes white out when she's actually creating storms, or the elements of storms. Not when she's just making wind.
And since, prior to X3, we never really saw her fly without lightning, thunder, etc present as well, we don't really know if she has to concentrate that hard to summon only wind. It would appear she doesn't based on the evidence.
Storm's flight abilities are not innate like Superman's: it takes controlled effort. Think about it: to hoist a 100-plus pound object in the air takes a significant gale force. That's why I mentioned the X1 elevator sequence: there was a LOT of wind moving which is why her decending on Toad looked all the more realistic and scary.
And that's all well and good, wanting the wind effects, but in the Danger Room sequence, there's a LOT going on in the scene. Multiple lasers, multiple explosions, sediment in the air. A more visible "wind" effect than Storm being carried herself and her cape billowing might have been a bit much to take in during that visually heavy sequence. But they did put in the billowing and the sound effect.
Of course, I respect one has to suspend some disbelief. But I do believe that X3's production was a bit inconsistent on those details. The production was so rushed. I also think the producers knew it too; that's why some of the worst examples got cut. One was a "tidal wave" sequence where Storm is floating in mid air and nothing is blowing at all.
I dunno...in that tidal wave sequence, her cape is billowing quite a lot as she rises into the air AND you can hear the wind sound effect as she takes off. Her cape continues to oscillate while she's up there. The deleted "tidal wave" sequence has a single brief shot where her cape doesn't appear to be blowing much, but its still sort of moving. And that could even be down to the fact that its raining around her, and the cape might just be weighted down or something.