I believe the Bible teaches that all of God's ways are perfect, so he never regrets something he does because it was wrong or a mistake. (Numbers 23:19) In Hebrew, to feel regret can mean to change one's mind or intention, based on a change in circumstances. For example, when the wicked Ninevites repented when Jonah warned them of imminent destruction, "When the true God saw what they did, how they had turned back from their evil ways, he reconsidered [or felt regret over] the calamity that he said he would bring on them, and he did not bring it." (Jonah 3:10)Well, if you take having regret indicative of having done something bad or a misdeed, we have.
Gen. 6:6
The LORD regretted that he had made human beings on the earth, and his heart was deeply troubled.
1 Sam 15:35
Until the day Samuel died, he did not go to see Saul again, though Samuel mourned for him. And the Lord regretted that he had made Saul king over Israel.
And even though Gen 8:20-22 doesn't say god regretted what he did, saying he would never do it again may suggests regret.
And, of course, there are all the killings of innocent lives he committed, which almost everyone considers to be bad.
20 Then Noah built an altar to the Lord and, taking some of all the clean animals and clean birds, he sacrificed burnt offerings on it. 21 The Lord smelled the pleasing aroma and said in his heart: “Never again will I curse the ground because of humans, even though every inclination of the human heart is evil from childhood. And never again will I destroy all living creatures, as I have done.
22 “As long as the earth endures,
seedtime and harvest,
cold and heat,
summer and winter,
day and night
will never cease.”
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Only in this sense does the true God feel regret. As our Creator, I believe Jehovah has every right to decide who merits death. Most people do not realize our true condition before God. (Ephesians 2:1-5) As Abraham said to God, "It is unthinkable that you would act in this manner by putting the righteous man to death with the wicked one so that the outcome for the righteous man and the wicked is the same!" (Genesis 18:25)