For one thing, most spell checking programs will not point out a correctly spelled word used in error of another word, if grammatically correct. For example, I might do a typo and type: foe, instead of, for. Let's say that I wanted to write: "What for?" But end up with,"What foe?" While there is no misspelling, it is not what I'd intended to write and would therefore be incorrect.
"I am going to the store."
The overuse of the same word is also overlooked with spelling and grammar check programs. For example: I might use the word, slipped, several times in just a few sentences. "Mary nearly slipped on the slick sidewalk. It was late when she got home and she quietly slipped in the door up to her room. She was grateful to be warm and cozy as she slipped under the soft blanket."
Capitalizing a word incorrectly is also overlooked. For example, "The Bishop went looking for his hat." No need to capitalize 'bishop' unless it is used as part of the person's name. Example: "Bishop Riley, will you be going too?" A proofreader could catch that error whereas the spell check program won't.
There are also errors in the transposition of words. "It was a beach day" might be accidentally written as, "It was a day beach." Or, "I love vanilla ice cream," might come out as, "I love ice vanilla cream."
And not to forget the number of words that have two acceptable spellings. I always like it when I think I misspelled a word only to learn there are two correct spellings. For example, the word, blonde, can also be spelled, blond. Blonde with the 'e' is often used to describe the color of a woman's hair, while blond without the 'e' is used mainly for males. It has been said that some consider the word "blonde" to be a sexist term and have dropped the 'e' in all usages. Donut/doughnut is another example. Donut is an informal variant of doughnut. There are many others. To see more, go to the following Wikipedia web site: http://en.wikipedia.org/wiki/Wikipedia:List_of_spelling_variants
Finally, there are always those tricky word spellings that warrant a dictionary check. Better safe than sorry.
I still remember the little ditty that we learned in English class in grade school: "Put 'i' before 'e' except after 'c' and when sounded as 'a' as in neighbor and weigh."
And, since this is a post on spelling errors, I better check it over several times. How did I do?