Correcting a paper that just came back from review, what should I do? After this one paper came back with minor revisions requested, I'm revisiting my data and making sure to check that everything stated in the paper is factual.

Finally, I found a few errors that were not pointed out by the reviewers and need correction.

The first error is that one of the charts had inaccurate error bars, which are much smaller now after the correction and actually support further my conclusions.

The second thing that I want to improve, which is not an error per se, is to get a new set of data for one of the graphs to substitute the current one which has an outlier point.

None of these corrections would alter the final conclusions of the study.

Since these corrections were not requested by the reviewers, I'm afraid the reviewers and the editor might think that this is inappropriate and will end up requesting another round of revisions or, even worse, rejecting the paper...

How do you think that the editor would take these unsolicited changes?
If you can justify the changes, there's no problem with making them. The first error for example should be clearly acceptable, if you said you performed error analysis in this way and it turned out there's a bug in your code.

The second is more dicey. Superficially, it might seem like you're altering your data because you have an outlier point (ergo, it's confirmation bias). You will need a convincing explanation why the new data set is better than the old one, why the outlier should not matter, etc.

In any case, if you make these kind of unsolicited changes, do be clear about them in your response to reviewers / cover letter. Otherwise, reviewers would have to read the entire paper again.