What should I do if I realize there is a minor error in a paper I submitted?

In order to answer this question, we need to define some magnitudes of errors.

A small error does not affect the conclusions and if the manuscript was accepted as is could be fixed in the proof stage before the manuscript goes to press.

A minor error does not affect the conclusions but requires too many changes to be made that it could not be fixed in the proof stage.

A substantial error affects the conclusions and would require the manuscript to be re-reviewed.

If you have found a substantial error, you need to contact the editor and request the manuscript be pulled from the review process. You do not want to waste the time of the editor and reviewers. A small error can either be ignored or reported to the editor if you think that the correction will help save the reviewers time. Minor errors are the real problem. There is no easy way to tell the editor/reviewer what is wrong, but an unclear manuscript is likely to get negative reviews. I would suggest contacting the editor and explaining and apologizing for the problem.

The real question should be how did you find the error? What are you doing looking at a manuscript after it has been submitted?

What if you have submitted a[n]... article ... that has a slight error?

You're answering your own question. If it's slight, then it's slight, and should not matter much.

Still, to be more practical: If

• The error, despite its slightness, means a significant claim is invalid, and
• The "distance" from the submitted version to the corrected version is small (e.g. replace a sentence, change a couple of numbers etc.), and
• You've just now submitted the paper (i.e. not weeks ago)

then I might describe a correction, in at most one paragraph of text (hopefully much less), and would write the PC chair to ask whether that can be passed on to the reviewers.

In all other cases I'd just wait it out and see.

Would it cause the rejection of my paper?

If the error is indeed slight, then this is very unlikely. But if your theorem says "P = NP" and you typed "=" instead of "!=", then maybe it will be rejected :-)

Seriously, though, the only cases I think this could have any weight is:

• Clueless reviewer who loses track of the flow of the paper because of the slight mistake, and thinks you've derailed yourself with it
• The slight mistake being accompanied by several other mistakes, slight or otherwise, so the submission is perceived as having numerous mistakes (regardless of their severity).