Dangling modifier: a modifying word or phrase that is not properly matched with the word it modifies. Dangling modifiers often occur at the beginnings of sentences.

Incorrect: Traveling north, the trees get smaller.

In this sentence, traveling north is meant to describe the person who travels, but instead it describes trees, which don't travel at all. One correct version would be:

Correct: Traveling north, I notice that the trees get smaller.

Squinting modifier: a modifier that is placed ambiguously, so that it is unclear whether it modifies the word before it or the word after it.

Incorrect: People who travel in Europe often prefer to stay in affordable hotels.

This could mean either People who travel often in Europe prefer to stay in affordable hotels or Often, people who travel in Europe prefer to stay in affordable hotels.

Pronoun confusion: pronouns that do not have clear antecedents make sentences confusing.

Incorrect: Jacob called a neighbor to ask about his car.

His could refer to Jacob or the neighbor. A correct version would be:

Correct: Jacob called a neighbor to ask about the neighbor's car.

Split infinitives: when possible, no words should come between to and the main verb in an infinitive.

Incorrect: He decided to boldly go where no man had gone before.

Correct: He decided to go boldly where no man had gone before.

Comma splicing: Joining two independent clauses with a comma rather than a semicolon or period creates a run-on sentence.

Incorrect: Many people think I'm tall, they don't realize I wear platform shoes.

Correct: Many people think I'm tall; they don't realize I wear platform shoes.

Correct: Many people think I'm tall.  They don't realize I wear platform shoes.

Double negatives: When applied to the same word or phrase, two negative modifiers confuse the meaning of the sentence.

Incorrect: I haven't hardly begun to think of my plans for next year.

Correct: I have hardly begun to think of my plans for next year.