user16626: For example, instead of capturing (and therefore exchanging) the queen on d8, white moved his queen from d1 to d7, and black can capture this queen for free. This is very likely the result of a misclick by white. Another example is moving the king for no reason in the opening stage. In this case, is it considered good etiquette for black to offer the draw, instead of taking advantage of white's misclick?
Some possible exceptions: 

My position is already winning before my opponent's misclick.
My position is still losing even after my opponent's misclick.
My opponent made a blunder which does not seem to be a  misclick.
My opponent demonstrated bad sportsmanship before misclicking.

In all above four cases, I will not offer draw. 

user17425: I consider that managing your mouse is one of the skills of online chess.  I'll take the win. 

user21807: First of all, if an opponent misclicks, you should also misclick to even the score. second. If the game is very important, then you should win.

user12523: An alternative if you want to be nice when your opponent misclicks is to make a waiting move. You might still benefit a bit from the tempo, but certainly not as much as if you had taken advantage of the blunder. For example, if White played Qd7 when the intent was clearly Qxd8, Black might play a relatively innocent move such as ...a6, so White can then play the intended Qxd8.
[Note: the above specific example might not be possible if the black king is in e8, as is likely the case! :-)]

user21823: I like to enjoy my chess. Equally so, I like my opponent to enjoy their chess too. If I feel like a misclick has spoiled the fun or if I'm winning because of a misclick, then I'll offer the draw.
There's a simple test for this. After that misclick, will you feel bad about winning the game? Check in with yourself about it. Your conscience is perfectly capable of determining the correct course of action for you at any given moment. Generalizing this is only going to cause suffering!

user19877: The most common term for that is actually a "mouse-slip".
Mouse-slips are dealt with differently by different players. There is no right or wrong answer since it is a personal decision. Some players on the Internet Chess Club used to put in their notes "no takebacks", meaning that if you had a mouse-slip, it was too bad for you.
For me, when I played blitz online, I played for fun, and I liked to be nice, but it would depend on the position. If the person were already dead lost, and maybe should already resign, I might just keep that queen, but otherwise, I would offer a takeback on ICC. You are also correct that if the opponent already had a bad reputation with me, I also might not be as inclined to give a takeback.
Since chess.com does not have takebacks, as for what I would do today, you can substitute a draw offer instead. 
How you handle it is really up to you, and how you feel about the exact circumstances of the game.

user307: It is perfectly good etiquette. 
Something similar happened in an Amber blindfold Gelfand - Kramnik:
[FEN ""]

1. d4 d5 2. c4 c6 3. Nf3 Nf6 4. e3 Bg4 5. h3 Bxf3 6. Qxf3 e6
7. Nc3 Nbd7 8. Bd2 Bb4 9. Bd3 O-O 10. a3 Ba5 11. O-O Re8
12. b4 Bc7 13. cxd5 exd5 14. b5 Nf8 15. bxc6 bxc6 16. Qd1 Ne6
17. Qa4 c5 18. Nb5 Bb6 19. dxc5 Nxc5 20. Qc2 Nfe4 21. Bb4 Nxd3
22. Qxd3 Qd7 23. Nc3 Qe6 24. Qxe4 1/2-1/2


"In case you wonder if the final move of the blindfold game between Boris Gelfand and Vladimir Kramnik was really 24.Qxe4 and if the result was nevertheless a draw despite White blundering his queen, we can tell you that in both cases the answer is affirmative. In the position after his 23rd move, Kramnik was expecting Gelfand to play 24.Nxe4 and after this move he intended to offer a draw. However, due to a ‘fingerfehler’, Gelfand didn’t move the knight to e4 but his queen. Kramnik understood what had happened and having no wish to win in such a manner he offered a draw anyhow. As Gelfand put it after the game: ‘He is a gentleman."


user20163: Just to offer a different answer:
No. No takebacks, no draw offers. In short time controls this is part of the game. It's the same as a blunder under pressure. I pressured the opponent on either time or position, and the person cracked and made a mistake.
Or your other example, of moving the king instead of castling in the beginning: That's what one get for trying to blitz out moves. Might save you a second here and there, but the risk is these mis-clicks. That's a price my opponent will have to pay, can't have the cake and eat it too.
(For longer time controls (1h+) I might think trying to salvage the game is the right choice, but I only really play 5min and below)

16626: <p>For example, instead of capturing (and therefore exchanging) the queen on d8, white moved his queen from d1 to d7, and black can capture this queen for free. This is very likely the result of a misclick by white. Another example is moving the king for no reason in the opening stage. In this case, is it considered good etiquette for black to offer the draw, instead of taking advantage of white's misclick?</p>

<p>Some possible exceptions: </p>

<ol>
<li>My position is already winning before my opponent's misclick.</li>
<li>My position is still losing even after my opponent's misclick.</li>
<li>My opponent made a blunder which does not seem to be a  misclick.</li>
<li>My opponent demonstrated bad sportsmanship before misclicking.</li>
</ol>

<p>In all above four cases, I will not offer draw. </p>
 17425: <p>I consider that managing your mouse is one of the skills of online chess.  I'll take the win. </p>
 21807: <p>First of all, if an opponent misclicks, you should also misclick to even the score. second. If the game is very important, then you should win.</p>
 12523: <p>An alternative if you want to be nice when your opponent misclicks is to make a waiting move. You might still benefit a bit from the tempo, but certainly not as much as if you had taken advantage of the blunder. For example, if White played Qd7 when the intent was clearly Qxd8, Black might play a relatively innocent move such as ...a6, so White can then play the intended Qxd8.</p>

<p>[Note: the above specific example might not be possible if the black king is in e8, as is likely the case! :-)]</p>
 21823: <p>I like to enjoy my chess. Equally so, I like my opponent to enjoy their chess too. If I feel like a misclick has spoiled the fun or if I'm winning <em>because</em> of a misclick, then I'll offer the draw.</p>
<p>There's a simple test for this. After that misclick, will you feel bad about winning the game? Check in with yourself about it. Your conscience is perfectly capable of determining the correct course of action <em>for you</em> at any given moment. Generalizing this is only going to cause suffering!</p>
 19877: <p>The most common term for that is actually a "mouse-slip".</p>

<p>Mouse-slips are dealt with differently by different players. There is no right or wrong answer since it is a personal decision. Some players on the Internet Chess Club used to put in their notes "no takebacks", meaning that if you had a mouse-slip, it was too bad for you.</p>

<p>For me, when I played blitz online, I played for fun, and I liked to be nice, but it would depend on the position. If the person were already dead lost, and maybe should already resign, I might just keep that queen, but otherwise, I would offer a takeback on ICC. You are also correct that if the opponent already had a bad reputation with me, I also might not be as inclined to give a takeback.</p>

<p>Since chess.com does not have takebacks, as for what I would do today, you can substitute a draw offer instead. </p>

<p>How you handle it is really up to you, and how you feel about the exact circumstances of the game.</p>
 307: <p>It is perfectly good etiquette. </p>

<p>Something similar happened in an Amber blindfold <a href="https://www.chessgames.com/perl/chessgame?gid=1488162" rel="noreferrer">Gelfand - Kramnik</a>:</p>

<pre><code>[FEN ""]

1. d4 d5 2. c4 c6 3. Nf3 Nf6 4. e3 Bg4 5. h3 Bxf3 6. Qxf3 e6
7. Nc3 Nbd7 8. Bd2 Bb4 9. Bd3 O-O 10. a3 Ba5 11. O-O Re8
12. b4 Bc7 13. cxd5 exd5 14. b5 Nf8 15. bxc6 bxc6 16. Qd1 Ne6
17. Qa4 c5 18. Nb5 Bb6 19. dxc5 Nxc5 20. Qc2 Nfe4 21. Bb4 Nxd3
22. Qxd3 Qd7 23. Nc3 Qe6 24. Qxe4 1/2-1/2
</code></pre>

<blockquote>
  <p>"In case you wonder if the final move of the blindfold game between Boris Gelfand and Vladimir Kramnik was really 24.Qxe4 and if the result was nevertheless a draw despite White blundering his queen, we can tell you that in both cases the answer is affirmative. In the position after his 23rd move, Kramnik was expecting Gelfand to play 24.Nxe4 and after this move he intended to offer a draw. However, due to a ‘fingerfehler’, Gelfand didn’t move the knight to e4 but his queen. Kramnik understood what had happened and having no wish to win in such a manner he offered a draw anyhow. As Gelfand put it after the game: ‘He is a gentleman."</p>
</blockquote>
 20163: <p>Just to offer a different answer:</p>
<p>No. No takebacks, no draw offers. In short time controls this is part of the game. It's the same as a blunder under pressure. I pressured the opponent on either time or position, and the person cracked and made a mistake.</p>
<p>Or your other example, of moving the king instead of castling in the beginning: That's what one get for trying to blitz out moves. Might save you a second here and there, but the risk is these mis-clicks. That's a price my opponent will have to pay, can't have the cake and eat it too.</p>
<p>(For longer time controls (1h+) I might think trying to salvage the game is the right choice, but I only really play 5min and below)</p>
