Rejoice not when thine enemy falleth, (into this mischief), and let not thine heart be glad when he stumbleth - When he meets with any thing that injures him; for God will not have thee to avenge thyself, or feel any disposition contrary to love; for if thou do, the Lord will be angry, and may turn away his wrath from him, and pour it out on thee.
This I believe to be the true sense of these verses: but we must return to the sixteenth, as that has been most sinfully misrepresented.
For a just man falleth seven times - That is, say many, "the most righteous man in the world sins seven times a day on an average." Solomon does not say so: -
1. There is not a word about sin in the text.
2. The word day is not in the Hebrew text, nor in any of the versions.
3. The word יפול yippol, from נפל naphal, to fall, is never applied to sin.
4. When set in opposition to the words riseth up, it merely applies to affliction or calamity. See Micah 7:8; Amos 8:4; Jeremiah 25:27; and Psalm 34:19, Psalm 34:20. "The righteous falls into trouble." See above.
Mr. Holden has a very judicious note on this passage: "Injure not a righteous man; for, though he frequently falls into distress, yet, by the superintending care of Providence, 'he riseth up again,' is delivered from his distress, while the wicked are overwhelmed with their misfortunes. That this is the meaning is plain from the preceding and following verses: yet some expound it by the just man often relapsing into sin, and recovering from it; nay, it has even been adduced to prove the doctrine of the final perseverance of the elect. But נפל is never used for falling into sin, but into distress and affliction - as Proverbs 11:5, Proverbs 11:14; Proverbs 13:17; Proverbs 17:20; Proverbs 26:27; Proverbs 28:10, Proverbs 28:14, Proverbs 28:18."

Rejoice not when thine enemy falleth,.... These words are spoken not to the wicked man, Proverbs 24:15; but to the just man, or Solomon's son, or the children of Wisdom; for by the "enemy" is meant such who are at enmity with the people of God, as the seed of the serpent, and those after the flesh, are: and when these "fall", saints should not "rejoice"; as when they fall into sin; for so to do would be to act as wicked "charity which rejoiceth not in iniquity", 1-Corinthians 13:6, or rather when they fill into calamity and distress; for this is also the part which wicked men act towards the people of God, and should not be imitated in; see Obadiah 1:12. Joy may be expressed at the fall of the public enemies of God and his people, as was by the Israelites at the destruction of Pharaoh and his host, Exodus 15:1; and as will be by the church at the destruction of antichrist, and which they are called upon to do, Revelation 18:20; partly on account of their own deliverance and safety, and chiefly because of the glory of God, and of his justice displayed therein; see Psalm 58:10; but as private revenge is not to be sought, nor acted, so joy at the calamity and ruin of a private enemy, or a man's own enemy, should not be expressed; but rather he is to be pitied and helped; see Proverbs 25:21; for to love an enemy, and show regard to him, is the doctrine both of the Old and of the New Testament;
and let not thine heart be glad when he stumbleth; even secret joy should not be indulged, gladness in the heart, though it does not appear in the countenance, and is not expressed in words; no, not at the least appearance of mischief, when he only stumbles and is ready to fall; and much less should there be exultation and rejoicings made in an open manner at the utter ruin of him.

The pleasure we are apt to take in the troubles of an enemy is forbidden.

Yet let none rejoice over the fate of evildoers, lest God punish their wrong spirit by relieving the sufferer (compare Proverbs 17:5; Job 31:29).

Warning against a vindictive disposition, and joy over its satisfaction.
17 At the fall of thine enemy rejoice not,
And at his overthrow let not thine heart be glad;
18 That Jahve see it not, and it be displeasing to Him,
And He turns away His anger from Him.
The Chethı̂b, which in itself, as the plur. of category, אויביך, might be tolerable, has 17b against it: with right, all interpreters adhere to the Kerı̂ אויבך (with i from ē in doubled close syllable, as in the like Kerı̂, 1-Samuel 24:5). וּבבּשׁלו, for וּבהכּשׁלו, is the syncope usual in the inf. Niph. and Hiph., which in Niph. occurs only once with the initial guttural (as בּעטף) or half guttural (לראות). רעו is not adj. here as at 1-Samuel 25:3, but perf. with the force of a fut. (Symmachus: καὶ μὴ ἀρέσῃ ἐνώπιον αὐτοῦ). The proverb extends the duty of love even to an enemy; for it requires that we do good to him and not evil, and warns against rejoicing when evil befalls him. Hitzig, indeed, supposes that the noble morality which is expressed in Proverbs 24:17 is limited to a moderate extent by the motive assigned in 18b. Certainly the poet means to say that God could easily give a gracious turn for the better, as to the punishment of the wicked, to the decree of his anger against his enemy; but his meaning is not this, that one, from joy at the misfortune of others, ought to desist from interrupting the process of the destruction of his enemy, and let it go on to its end; but much rather, that one ought to abstain from this joy, so as not to experience the manifestation of God's displeasure thereat, but His granting grace to him against whom we rejoice to see God's anger go forth.
(Note: This proverb, according to Aboth iv. 24, was the motto of that Samuel with the surname הקטן, who formulated ברכת המינים (the interpolation in the Schemone-Esre prayer directed against the schismatics): he thus distinguished between private enemies and the enemies of the truth.)

Falleth - Into mischief.