Yes, a button to finish the level is a good idea. With "TEST!" or "TIMBER!" as call to action or something.
And yes, the level generation could use a lot of additional tweaking. I have only thought of 1 trick to remove extraneous lines. Which is when a dot is straight below another dot. Then it only needs 1 line straight down. In level 55 there is just a small base and too many dots on the right side. I think in that case I need to remove some dots to balance the center of the mass again. Those hanging dots also give a little more extra weight.