The teacher’s involvement would interrupt the flow of pair work or a group activity.
The error can be addressed momentarily by back tracking a little bit.
The student can somehow be prompted to self correct their own error[Read Deeper: How to Push Students to Self Correct Their Own Mistakes]
The error made goes significantly beyond the student’s current capabilities in English.
The error shows they don’t understand a language point you plan to teach in the future.
The error is fossilized, student is well aware of the error, pointing it out would only frustrate them.
The student showed great improvement in another aspect of their answer and you want to give them a clear win.
Correcting the error may knock their confidence in the current situation.(They are already having a bad day, uncomfortable speaking in front of the class, etc.)
The focus of the lesson is on listening or reading comprehension, not on accuracy in spoken English.
You have prepared and will soon use an expected list of errors to be made and theirs is on that list.
More about it : http://yourenglishsource.com/good-reasons-not-to-correct-students/