Subjective applies to things that are based upon an opinion. Subjective is defined as...
...existing in the mind; belonging to the thinking subject rather than to the object of thought.
In other words, something subjective is based upon one's feelings or opinions. There is no right or wrong perception. This is as opposed to objective, which is not given to opinion, but based on fact. The fact that the sun is the closest star to the earth is objective. Stating that a friend's hat is ugly is subjective: based on one's opinion.
Subjective writing focuses on the view from inside the writer's mind. Objective writing tries to focus on the view of objects from the outside.
In referring to Shakespeare's sonnets, anything based upon one's feelings is subjective. Anything based upon fact is objective. As an example, to note that Shakespeare's sonnets all contain 14 lines would be objective. Saying that they are the best things ever written is a matter of opinion, not fact.
In terms of subjective elements, look to Sonnet 18 first. It begins:
Shall I compare thee to a summer's day?
Thou art more lovely and more temperate...
The speaker notes that "she" (the subject of the poem) is lovelier than a summer's day, and more comfortable. This is based on the speaker's opinion. Noting that as long as there are men alive to read his sonnet, her beauty will not fade. This is all subjective. For what one man sees as beautiful may be different for another man.
Sonnet 65 begins with what seems to be a highly arguable concept: that mortality is greater than the mightiest aspects of nature.
Since brass, nor stone, nor earth, nor boundless sea,
But sad mortality o'er-sways their power...
This statement reminds of me of the philosophical question: if a tree falls in the woods and there is no one there to hear it, does it still make a sound? If mankind were gone from the face of the earth, would not stone, brass, earth, or the "boundless sea" still be as powerful? Because this is not based upon fact, it must be subjective.
Sonnet 97 is based upon the speaker's opinion, but how could someone argue his point for it is based upon what is true for him! There is no sweeping generalization, but his own experience:
How like a winter hath my absence been
From thee, the pleasure of the fleeting year!
What freezings have I felt, what dark days seen!
However, in coming from feelings, it must be subjective.
Sonnet 106 has subjective elements in that the speaker imagines what people from the past would think about the woman he is speaking to, and her beauty. There is no way to ascertain their opinions for certain.
I see their ántique pen would have expressed
Ev'n such a beauty as you master now.
No one can look into the past and be certain that writers long dead would feel or say about the beauty of this woman in the present: there are no facts here.
Sonnet 116, although a truly beautiful poem, is filled with subjective elements. This is clearly seen as the speaker tries to define what love is. Poets and writers have been attempting to do this for centuries. Love means different things to different people. And while we may agree with what is said, it is based upon opinion, and therefore, is subjective.
Love is not love
Which alters when it alteration finds,
Or bends with the remover to remove:
O no! it is an ever-fixed mark...
We might wish love to never change or alter, but that's an opinion.