Are there any mistakes in this introductory paragraph?

Question

I think I’ve found two mistakes in this introduction:

Parents play an important role in the child’s upbringing. However, it is not easy to be a good parent, much to the surprise of those who think dealing with young children is a piece of cake. In my view, to be a good parent you have to meet certain requirements that I am going to discuss further in the following paragraphs.

The first should be: much of a surprise to those who think

For the second, I think further is not appropriate because here it is in the introduction, so the speaker hasn’t discuss anything. It should be: discuss in details.

Answer 1

I am afraid you got the wrong end of the stick. As for much to the surprise of those who think is grammatically correct. Consider the following expressions:

to be much to one's amusement (They were dancing and singing in the car, much to the amusement of passers-by.)

to be much to the consternation of somebody (A new power station is being built much to the consternation of environmental groups.)

or

to be [very much] to one's liking (formal - if something is to someone's liking, they like it or think it is satisfactory)

This kind of film is to my liking, I have always liked horror.

As you can see, the structure of to be much to ... is grammatically correct. What you may have been bedazzled by is that the preposition is strange. You are right, but a collocation has its own strange structure that you cannot change.

It was much of a surprise to me that she chatted that guy up. (It surprised me.)

It was much to the surprise of mine (or simply to my surprise) that she chatted that guy up. (it is the same here but does sound strange, however, in your sentence it is normal)

As for further, bear in mind that farther refers to space (a greater distance than before or than something else; a comparative form of far), further refers to everything else (e.g. it has the meaning of more, something in connection with time, in addition).

Answer 2

Restricting my answer to the propriety of "further discuss" (because "much to" has been fully covered in another answer), there is nothing grammatically or idiomatically incorrect about it. As is typical in an introductory paragraph, you are clarifying what you intend to discuss. "Discuss further" is no more and no less redundant and formulaic than "discuss in detail." (By the way "discuss in details" is not idiomatic in the U.S.)

I suspect that what is bothering you has nothing to do with grammatical or idiomatic English, but rather a sense that the sentence is verbose and uninteresting. In other words, you are developing a sense of English style. So here is a more succinct sentence that might spark your audience's interest.

A good parent must meet certain requirements, not all of which are obvious.

You do not need to say "in your view" because who else's view can you be expressing. You do not need to say "discuss further" or "discuss in detail" because it is clear that you have not discussed anything yet. A good introductory paragraph states what the topic will be and provokes the reader to continue.