Take a look at the sentence again:
Rachel painstakingly ironed her linen shirt all
the while, she was thinking how pointless this chore was since linen begins
to wrinkle the moment after the last button is fastened.
The problem occurs between shirt and all. Rachel painstakingly ironed her linen shirt is a main clause, so it can stand alone as a complete sentence. All the while, she was thinking … begins the next complete sentence. Because these two parts have only blank space between them, they make a fused sentence, a major error.
To fix the problem, you could put a period after shirt and then capitalize the A for all.