What is the danger of high compression in a spark ignition engine?

If the pressure is too high for the grade of fuel, you will get 'pinking' or 'pinging'. This is the term for pre-ignition. The fuel will explode instead of burning rapidly, and makes a metallic rattling or 'pinking' sound.

This can damage the valves and piston crown if left to continue.

High compression engines need a better grade of fuel, a higher Octane number.