For one example of how the comparison breaks down, consider the cost of adding up a page full of numbers in 1950 vs. today. In 1950, you'd need to hire an accounting clerk. Nowadays it's essentially free. In 1950, the clerk would have added the value of his labour to GDP, Today, the computer doing the same job contributes little or nothing.
The same problem crops up everywhere. If I develop a $1000/month treatement for hepatitis, I might add a vast amount to GDP. If I develop a $5 one-off cure, not so much.
GDP can't 'see' goods and services that are so cheap to produce that they're practically free.