We come across two sorts of incompleteness if you regard language as means to represent the world faithfully and communicate it to others. This incompleteness is, however, necessary for us.
1. Language selects its object
It often irritates us that we cannot describe moving experience accurately. Language is universal, while reality is individual. You must feel something wanted, when you describe a scenic spot just as land of exquisite beauty. So, people often complain of this incompleteness of language and wish language were more expressive and complete.
But if language were a completely faithful picture of reality, language would not be distinguishable from reality, namely no longer necessary. We need language, because it abstracts reality.
As cerebral capability to process information is restricted, language cannot but throw away the majority of actual diversity and gather only the minimum information required for survival.
2. The selection is various among people
It depends, however, on each individual to decide what to abstract. It follows the meaning of words differs delicately among users. This is the second incompleteness of language. In communication, the difference in the meaning of language can be a cause of misapprehension, which often induces quarrels and wars. So, people often complain of this incompleteness of language and wish we had the same definition of words and did not need to quarrel because of misapprehension.
Now that there are no determinate criteria as to what is the minimum information for survival, it is necessary for our species to survive that various ways of abstraction should be tested by natural selection. Since how we define words is inseparable from our thought and values, fixing the meaning of words uniformly is not desirable for our knowledge to develop.
Thus, although our language has two kinds of incompleteness, it is not the defect to be corrected. It rather contributes to maintaining and developing our species.