Often writers intend for a clause or phrase to modify one element in the sentence, but the placement of the modifier actually causes it to modify a different element.
UNCLEAR: My English professor is a unique-looking man with crazy white hair, standing about 6 feet 6 inches tall.
The last clause, standing about 6 feet 6 inches tall, obviously refers to the professor, but because of the way it's placed in the sentence it actually refers to his hair. To convey the desired meaning, it needs to be rephrased:
REVISED: My English professor, who stands about 6 feet 6 inches tall, is a unique-looking man with crazy white hair.
These are modifiers that could refer to more than one element in the sentence but that would change the meaning based on which element they modify.
UNCLEAR: The woman who works at the farm stand where I buy my vegetables occasionally asks me about my family.
There are two possible readings of this sentence because it's not clear what is happening occasionally. Either the writer occasionally buys his vegetables at a certain farm stand, or the woman at the farm stand occasionally asks him about his family. To get one meaning or the other, the sentence would have to be rephrased in one of the following ways:
REVISED: The woman who works at the farm stand where I occasionally buy my vegetables asks me about my family.
REVISED: The woman who works at the farm stand where I buy my vegetables asks me about my family occasionally.
These disrupt the flow of a sentence by being placed between subject and verb or verb and object.
AWKWARD: My little brother, when his teacher threatened to kick him out of class if he didn't start behaving, shaped up.
By the time you're finished reading the long modifier, you've probably forgotten whom it's even talking about. Rephrase:
REVISED: When his teacher threatened to kick him out of class if he didn't start behaving, my little brother shaped up.
These do not logically refer to any word appearing in the sentence. They usually suggest an actor but do not actually name it.
ILLOGICAL: Flying in the helicopter, the cows in the field looked tiny.
According to this sentence, the cows are flying in the helicopter. Clearly this is not the intended meaning, but the correct subject is missing. Revise:
REVISED: Flying in the helicopter, we thought the cows in the field looked tiny.