Example One:
'At the age of six, my father took me to his office for the first time.'
This sentence contains a participial phrase, which is meant to modify a subject that is missing from the sentence. The modifier is then dangling, meaning that there's no way to tell from the words themselves exactly who was six years old.
Of course, logically the reader assumes that it was the speaker who was a child when visiting the father's office. But since we are trying to make our writing as clear as possible, we need to add a subject to clear up the confusion.
'When I was six years old, my father took me to his office for the first time.'
Example Two:
'A woman passed by, leading a bulldog in a fluffy pink dress.'
In this sentence, the modifier is the prepositional phrase at the end of the sentence: in a fluffy pink dress. As you may have noticed, modifier mistakes often lead to humorous mental images.
Of course, this probably is not what the speaker actually saw. It was probably the woman wearing the dress, and not the bulldog. So we can clear up this confusion simply by placing the modifier where it belongs: immediately following the noun it modifies.
'A woman in a fluffy pink dress passed by, leading a bulldog.'
OR
'A woman passed by wearing a fluffy pink dress and leading a bulldog.'
This second option is even better, because it exhibits more readable parallel structure, meaning that both the modifying phrase and the main verb phrase are expressed in the same format.
Example Three:
'Using high-powered binoculars, the lost boy was found on the trail.'
Again, if we really think about the intent of the speaker, we can guess that someone, perhaps park rangers or trail leaders, found a boy who was lost on the trail by using binoculars. However, there is the possibility here that it was the boy using the binoculars.
We can clear up this one by adding a subject to the modifying phrase, like this:
'Using high-powered binoculars, the rangers found the lost boy on the trail.'
Example Four:
'I found my missing baseball glove cleaning my room.'
In this sentence, there is something missing that will fix the problem. As it is, this statement seems to tell us that the baseball glove was cleaning the speaker's room! Even without an actual picture, you can probably imagine how ridiculous this action would be. So how can we change the sentence to show that the speaker was cleaning his or her room and, while doing so, found a missing baseball glove? How about this:
'While cleaning my room, I found my missing baseball glove.'
With the addition of an adverbial phrase at the beginning and the subject in the main part of the sentence (the independent clause), the sentence now reads clearly.