Pretty nifty overall. This seems like the kind of game I'd want to play for just a few minutes at a time, so the fewer screens and steps between launching the game and the action there are, the better. I thought it was enjoyable.
If I weren't already familiar with Plinko, I'd be lost. The tutorial goes into details too soon before the general gameplay. Do you even need a tutorial? Why not just drop the player right into level one. When they collect their first upgrade star, then lead them to the upgrade menu. Most of the upgrades seem simple enough that a well-designed icon should be sufficient to explain what it does.
There's no point in having a level select screen when there's only one level unlocked. So that's another screen you can skip in the early stage of the game.
I don't like the idea of a panic button. In my opinion, if the ball gets stuck on a "normal" structure, that's a fault in the level design. However, traps that are clearly such would be an interesting addition. Traps should be obvious, like a bucket, lava, etc. Losing a life feels fair that way.
Also a bug--sometimes it seems like I click to drop the ball and I lose a life or two.