Question

What if a mutation happens during protein synthesis? what happens?

Answer 1

then you get a malfunctional protein. Lol. it can either not function or function incorrectly.
it's not as bad as a mutation in the DNA framework since DNA is copied and eventually distributed throughout which can mess up the whole process after DNA is copied such as pre-translation and translation itself.

Answer 2

By mutation, do you mean mutation in the genetic information, or a misincorporation of an amino acid during translation? To answer your question I'm going to assume you mean that there is no mutation in the original genetic material, and that the incorrect amino acid was incorporated into the protein during protein synthesis.

It's really going to depend on the chemical properties of the amino acid that was incorrectly incorporated, and the chemical properties of the amino acid that was replaced. If two amino acids with very similar chemical properties were exchanged for one another then there might be no effects at all. For instance, valine and leucine are pretty similar to each other in structure, charge, and pKa and it's possible that this substitution wouldn't have any effect.

If, however, an amino acid that plays a critical role in the structure or function of the protein were replaced the result might be a non-functional protein. If you replace a hydrophobic amino acid like tryptophan with a hydrophilic amino acid such as glutamine the effects will be more drastic.