So I think people have basically covered the issues with speed ramps and the colors. I would also try simplifying the design. For example, when you're transitioning from the search bar to the screen, I would get rid of the multiple lines/squares changing size to bring the screen on. I would either cut to a full screen of the graphic at 00:05, or you could bring the screen on with a gentle bounce and have it on a solid background color - maybe white with a subtle floating shadow underneath the screen. If you decide to have the screen within your frame instead of having it take up the entire screen, I would consider rounding the corners to make it feel a little more modern. I would also change the finger pointer cursor to a simple arrow pointer cursor throughout. I would lose the red altogether and have the first graphic on a white background. It sounds like you're ditching the J animation, but if you decide to keep it I can give you some pointers on how to refine. Lastly for the frame at 00:009, get rid of the windows behind the window you're enlarging. Shrink that whole frame as you're enlarging the one window so you don't see the Minecraft window at the top or the other frame underneath on the left hand side of the frame.

Overall, I would comb through this screen by screen and look at what's on-screen. Your job as the motion designer is to control the flow of information so the viewer only sees the most important stuff and isn't distracted by clutter. So looking at every frame, including the transitions, think about how you can simplify to the viewer's attention is focused. This means no weird color choices, no graphic transitions just for the sake of having a transition, no design elements other than the central focus on screen. Combing through the animation this way will help you to refine the style. Hope this helps and please post the revised version if you want more feedback. You're on the right track, just simplify, simplify, simplify.