Not a problem.
The issue with the loose goggles is that they don't really read as 'loose' -- just as maybe out of sync with the character's body and physics. I'd suggest keeping the head-turn in sync with the goggles as in my edit, but perhaps animating them up/down a bit more exaggeratedly and perhaps have one side/eye of the goggles go up higher than the other on various frames as they bounce upward instead of them wobbling left to right. After all, when the foot hits the ground, it's possible one foot steps a little harder than the other periodically, thus causing that side of the goggles to bounce upward a pixel higher than the other side.
Regarding the wobbly-hat thingy, it's definitely cliche that I just exaggerated the cutesy look your sprite had, but the real intent was to give the top portion of the sprite a little more life since the hat makes up so much of his body. If you were to put a tear in the hat, perhaps you could make the ripped portion flop while he steps or the hat bounces/squashes/stretches or something -- anything to give it a little more interest, no matter if you're going for a 'lifeless/soulless' character or not.
And yeah, I wasn't aware of that being a robotic automation sort of thing -- still though, increased colors/contrast helps a lot, even if you go with all blues/purples and some grey to blend the the red/blue shadows. I see a lot of dullness when people overuse desaturation and greys in their sprites to convey 'dark' or 'gritty' and it generally comes off as simply uninteresting, dull, and lifeless instead -- despite it having amazing animation!
While making that edit I also noted that you have a lot of colors in your palette that are used only once or twice (with very VERY slight differences). That too can make your sprite look a bit odd without the viewer or artist ever really knowing why. When I did my first sprite anim frames in Photoshop way back in the day, this happened to me a lot and I'm not sure why (maybe because PS selects an average of the colors where you click with the eyedropper instead of the actual pixel color you clicked on maybe? I dunno.) Grabbing colors straight from the sprite with right-click in Graphics Gale, which I've used pretty much exclusively since then, helped me get over that.
That being said, great character design so far! I'd love to see what you do with it from here on. ^_^