“From the very beginning, however, one was not unprepared in this domain to come upon failure of the forms of perception adapted to our ordinary sense impressions.” 
Here, this domain refers to the atomic theory and Bohr admits that he was not unprepared for the alleged failure of the forms of perception. What could have lead one to be prepared for this? Philosophy.
“There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about Nature.” 
So, in other words, we cannot know physical reality, only abstract descriptions. Physics is not the study of reality as it is, but simply a pragmatic description that explains what we observe.
An abstract description of what? The next quote gives us a clue.
“We must be clear that when it comes to atoms, language can be used only as in poetry. The poet, too, is not nearly so concerned with describing facts as with creating images and establishing mental connections.” 
Here Bohr means that language can not be used as a precise method of the description of reality. The purpose of words, of concepts, of ideas is not to describe reality, but to describe and relate “images” and “mental connections”.
In other words, the purpose of language, of concepts, is not to study physical reality, but to study and relate abstractions.
So when we asked, “An abstract description of what?” Of, what? Nothing? Or perhaps abstract descriptions of sense perceptions. But sense perceptions of what? We shall return to this in a little bit.
Are these abstractions to be considered objective? Bohr does not think so.
“I consider those developments in physics during the last decades, which have shown how problematical such concepts as objective and subjective are, a great liberation of thought.” 
Bohr does not consider it worthwhile discussing whether or not an idea is objective or subjective. This is not too surprising given that one of Bohr’s many philosophical influences was, as we shall see, pragmatism.
You might ask whether there was any justification for Bohr saying these kinds of things. It is certainly widely asserted that Bohr and his peers were forced to reluctantly accept the implications of quantum theory.
But there can be no physical justification for claiming that reality is unknowable.
Why then did Bohr adopt this view? Is it because the quantum world really is “inflicted with a kind of vagueness”? Or, is it because of his philosophical influences?
“The situation which we meet here is characterized by the fact that we are apparently forced to choose between two mutually contradictory conceptions of the propagation of light. One, the idea of light waves, the other, the corpuscular [particle] view of the of the theory of light quanta, each conception expressing fundamental aspects of our experience. As we shall see in the following, this apparent dilemma marks a particular limitation of our forms of perception which is bound up with the quantum of action.” 
Are we forced to choose between contradictory conceptions of light? No. Objectivity, the recognition of reality as it really is, requires us to identify the fact that it can be only one of those and to attempt to identify which one is the case.
Far from it being a dilemma, it is a requirement of objectivity and identifying reality. To ignore this requirement is to reduce the concept of light to a floating abstraction and to make it impossible to identify its true nature.
Nor is it a limit of our “forms of perception” as such. Nothing that exists can exist with a contradictory nature. To be is to be something, free of contradictions.
Far from being a “limitation” of our “forms of perception” this is a necessary fact which everything, including perception, must adhere to.
“An independent reality in the ordinary physical sense can neither be ascribed to the phenomena or to the agencies of observation. After all, the concept of observation is so far arbitrary as it depends upon which objects are included in the system to be observed. Ultimately, every observation can, of course, be reduced to our sense perceptions.” 
Here Bohr advocates the idea that observation is not the observation of real entities in the physical world, but of floating sense perceptions. In his view, science is not the study of external physical reality, but the description of sense perceptions.
Sense perceptions of what? Reality does not begin with sense perception. To perceive is to perceive something.
Our senses do not distort that which they observe. Neither do our senses create their own content. But, Bohr frequently spoke as if he believed that our senses create their own content or distort that which they do observe.