This puzzle consists in scanning for a value (called Nonce) that when hashed, the hash begins with a number of zeros.
From this line it seems that the only hash input is the nonce. However, from my understanding, all block data is hashed. The only variable in this block of data is the nonce, therefore it can change the hash output.
The difficult in finding that nonce increases exponentially as more zeros are required by the block. Difficult is adjusted so that one block is mined every 10 minutes.
This sentence would be more clear if you would introduce the frequent term difficulty. Optionally, you can add that the difficulty only changes every 2016 blocks or average two weeks.
Despite this, I still find your summary very informative and accurate.