I routinely work with a number of writers with English as their second, third, or even fourth language. These guys and gals create fantastic content and often do very well with grammatical rules (especially the academic crowd). However, one area that remains a problem for just about all of them is words and phrases that simply do not translate.
I recently came across a few threads on reddit which discuss this very topic. Here are two of the favorites.
There are many more examples at r/doesnottranslate to demonstrate why it can be so beneficial for non-native speakers to have their material edited. These types of mistakes will not be caught by editing software alone. Even for less formal material, I would suggest having a native-speaking peer do a read-through. For anything that you’re planning to publish or turn in for a major grade – I highly suggest finding a professional editor.