Studying proteins, one is immediately confronted with Darwin's problem of 'extreme perfection' not once but many times over. Proteins are superbly designed. They have astonishing efficiency, precision and regulatory abilities.
Consider one 'typical' protein of around 300 amino acids. Each amino acid is one of 23 kinds. Changes to the DNA that codes for the protein may cause a different amino acid to be used in one position. This is called a point mutation. Many changes that could be made to that protein will cause it to no longer fold correctly, and consequently to be useless at its former role. Loss of function of even one kind of protein could prove lethal to the animal plant or bacterium that uses that protein.
Now take an analogy. Think of a 'one armed bandit' (in U.S. speak a 'gaming machine'). Normally these have around five wheels, pull the lever and hope for five bells or some other pay-out pattern. Our one armed bandit has 300 wheels, and each can show one of 23 patterns. When you pull the lever instead of all the wheels spinning only one will spin - which one spins is random. You start with 200 bells and you want to increase that to 201 bells. Fortunately for you, if you don't succeed at first you may get an extra go. In the protein analogy this corresponds to either a combination which represents a still functioning protein, or a relative who inherited the initial pattern unchanged and so survived. On average you'll need about 35 goes.
Now imagine that you are blindfolded so you can't see the one armed bandit display. Instead the one-armed-bandit makes a beep each time you are allowed to play again and the pitch of the beep changes almost imperceptibly depending on how many bells there are. You have to guess whether to keep the new pattern or to go with the old pattern. If your guesses here are nearly random, equally likely to make the right decison as the wrong one, then your chances of reaching 210 bells are slim indeed. You are 46 times more likely to slip from 200 bells to 199 as to step up to 201 on your first spin. That's the best I can do within this analogy for the selective advantages of a near-imperceptible change.
I hope the above analogy has given some idea of the difficulty evolution faces in finding 'good designs' for individual proteins. Some specific problems the example tries to bring out are: