Question: After solving the first few levels in Crayon Physics my "world map" looks like this:

![enter image description here](https://i.stack.imgur.com/jVTrg.jpg)

It appears I earned two flags on the first level, one flag on the following two, no flag for the fourth, then I earned two flags and... a ball.

Is that just cosmetic, or does it depend on how well I did? If so, how can I improve this score?

Answer: 
Those are cosmetic. Only the stars count.
You can i[mprove your score](http://www.kloonigames.com/blog/crayonphysics/crayon-physics-deluxe-gameplay-update) by finishing a round in one of the following ways.

1. Hole in one - for this, you have to get the star by drawing a single line
2. Old School, and - for this, you shouldn't touch the ball or draw any pins
3. Awesome - the user marks a solution "awesome".

You can look for some sample solutions on youtube walkthroughs for each. :)
If you have two flags on one level, you can click the level then the 'solutions tab' and mark your solution as 'awesome'. This gives you one orange flag for the level, and an extra star.