For example, if the programs flags an its or it's and tells me to use the other, it's unfailingly wrong. People make careless mistakes, but for a computer program to be wrong this often suggests to me that someone has mis-programmed it. That programmer also occasionally confuses there and they're or who's and whose, and regularly confuses lay and lie (again, wrong in both directions). For example, the grammar checker recommends ...to see in which way his sympathies might lay. Nice rhyme.
Sometimes the errors are understandable but funny all the same. For example, the program suggested I change Amidst the four seated judges to Amidst the four-seated judges I imagine the judges sitting there with incredibly broad laps, each with four large colleagues seated on his knees.
The grammar checker has a virulent dislike for reflexive verbs. To She examined herself in the mirror it would prefer, She examined her in the mirror. Meaning be damned. (That last sentence would undoubtedly be condemned as a fragment.)
The program gets nervous when it thinks it sees a double negative. For example, it suggested I change She saw nothing: no mountains, no trees... to She saw nothing: no mountains, any trees...
Most distressing to me, because I suspect it's the reason I see so much random use of semi-colons in online critique groups, is the grammar checker's irrational approach to this useful piece of punctuation. The rule of thumb seems to be that when a sentence reaches a certain length, the program wants semi-colons to replace at least one comma. Here are some examples of the sentences it wants:
"And her?" He gestured at Daphne without looking at her; something Ivan knew would make her furious.
Afraid she'd knock Daphne down; Ivan intercepted her.
When she was gone, Lila poked her head out from under the bed; her eyes and mouth round with excitement.
Ivan knelt among the other workers; pressing sprouts into the earth.
Daphne sat at Lila's feet; making vicious stabs at the lower-class sewing the shop owner had given her.
None of these sentences meet the requirements for using a semicolon; not one contains either a long list whose individual elements include commas or a pair of independent clauses--each a complete sentence in its own right--attached by a semi-colon to show a relationship between them.