The three most common sentence-level errors are the run-on sentence, the comma splice, and the sentence fragment.

The run-on sentence is the fusing of two independent clauses without using proper punctuation (a period or a semicolon) or without using an appropriate structure-class word (coordinator, subordinator, relative, nominal-that, interrogative, or conjunctive adverb) to create a grammatically correct structure.

• *Jenny hit the ball she ran to first. - Run-On
• Jenny hit the ball. She ran to first.
• Jenny hit the ball, and she ran to first.
• Jenny hit the ball, then she ran to first.

You should be able to recognize if two independent clauses are joined incorrectly. Let's use a variation on the same paragraph that we have been using:

Margot’s mind reeled. She could hear the listless, scraping sounds of fingertips against the door. It haunted her to consider the sea of faces outside. They were faces she once knew in a different light now they were putrid reflections of squalor and decay. There was nothing left for her to glean from their lifeless eyes except the grim reminder that she was alone. She tried to ignore the thought, but she was the last bastion of humanity death awaited her outside.

When we are searching for clauses, we first need to identify all main verb phrases:

Margot’s mind reeled. She could hear the listless, scraping sounds of fingertips against the door. It haunted her to consider the sea of faces outside. They were faces she once knew in a different light now they were putrid reflections of squalor and decay. There was nothing left for her to glean from their lifeless eyes except the grim reminder that she was alone. She tried to ignore the thought, but she was the last bastion of humanity death awaited her outside.

Once we know where the clauses are, we can, at this point, look specifically for run-on sentences: 

They were faces she once knew in a different light now they were putrid reflections of squalor and decay.

Run-On Sentence

• There are three clauses in this sentence, and the second one could be confused for a run-on, but is, instead, a deleted-that relative clause. The third clause, however, is clearly a run-on because it is an independent clause fused to the first independent clause.

She tried to ignore the thought, but she was the last bastion of humanity death awaited her outside.

Run-On Sentence

• There are three clauses in this sentence, as well, with a coordinating conjunction separating the first two independent clauses. The third clause, however, is clearly a run-on because it is an independent clause fused to the second independent clause.

NOTE: just because a sentence is loooooooong doesn't mean that it's a run-on sentence. A run-onsentence has a very specific definition: when two independent clauses are fused without proper punctuation.

The comma splice is a variation on the run-on in that it incorrectly separates two independent clauses with a comma.

• *Jenny hit the ball, she ran to first. - Comma Splice
• Jenny hit the ball. She ran to first.
• Jenny hit the ball, and she ran to first.
• Jenny hit the ball, then she ran to first.

You should be able to recognize if two independent clauses are joined incorrectly. Let's use a variation on the same paragraph that we have been using:

Margot’s mind reeled. She could hear the listless, scraping sounds of fingertips against the door, it haunted her to consider the sea of faces outside. They were faces she once knew in a different light, and now they were putrid reflections of squalor and decay. There was nothing left for her to glean from their lifeless eyes except the grim reminder that she was alone. She tried to ignore the thought, she was the last bastion of humanity. And death awaited her outside.

When we are searching for clauses, we first need to identify all main verb phrases:

Margot’s mind reeled. She could hear the listless, scraping sounds of fingertips against the door, it haunted her to consider the sea of faces outside. They were faces she once knew in a different light, and now they were putrid reflections of squalor and decay. There was nothing left for her to glean from their lifeless eyes except the grim reminder that she was alone. She tried to ignore the thought, she was the last bastion of humanity. And death awaited her outside.

Once we know where the clauses are, we can, at this point, look specifically for comma splices: 

She could hear the listless, scraping sounds of fingertips against the door, it haunted her to consider the sea of faces outside. 

Comma Splice

• Two independent clauses separated with a comma.

She tried to ignore the thought, she was the last bastion of humanity.

Comma Splice

• Two independent clauses separated with a comma.

Finally, the sentence fragment occurs when one of the primary clause constituents (subject or main verb phrase) is missing and it attempts to stand independently. Confusion about nonfinite verb phrases is probably the biggest culprit in creating fragments:

• *The listless, scraping sounds of fingertips against the door. - Fragment (No Main Verb Phrase)
• *Nothing left for her to glean from their lifeless eyes except that grim reminder. (No Main Verb Phrase)

More commonly, a sentence fragment occurs when a dependent clause is punctuated like an independent clause. As you know, a dependent clause cannot stand alone.

• *After she hit the ball. Jenny ran to first. - Fragment
• After she hit the ball, Jenny ran to first.

Writers sometimes use sentence fragments for rhetorical effect. While they are not grammatically complete clauses, sentence fragments can sometimes be appropriate in the context of the purpose, genre, and audience of a piece of writing. Rhetorically effective and appropriate sentence fragments typically occur more often in fictional and literary prose, rather than non-fictional and technical prose. In the example below from Virginia Woolf’s A Room of One’s Own, the sentence fragments function like indirect discourse to illustrate the yelling figures:

“And as I watched her lengthening out for the test, I saw, but hoped that she did not see, the bishops and the deans, the doctors and the professors, the patriarchs and the pedagogues all at her shouting warning and advice. You can’t do this and you shan’t do that! Fellows and scholars only allowed on the grass! Ladies not admitted without a letter of introduction! Aspiring and graceful female novelists this way! So they kept at her like the crowd at a fence on the race-course, and it was her trial to take her fence without looking to right or left.”