In the current standard text of the ma nishtana it states that at the seder we dip twice. But according to my count we dip three times, Karpas, Marror and Korech (either the whole sandwhich or just the marror part). How can we explain this discrepancy?
This question can be addressed by noting that there is a dispute among the rishonim whether Korech should get dipped at all. See Tur O.C. 475 with commentaries, and Shulchan Aruch there with commentaries. The opinion that states that Korech is not dipped says that there are only supposed to be two dippings.
וי"ל דאלו שנים של חרוסת הם נחשבים לא' דאין עושין כן אלא משום ספיקא
These two [dippings] of charoses are only counted as one, because we only do it out of doubt.
We do not count the korech part as a dipping in the sense that we mean for karpas and Maror. It is a זכר למקדש כהלל and a way of accomodating both views as to how the matza and maror must be eaten. Since only one of the methods is correct, we are still only dipping two times.
Alternatively, on a child's level, I would expect him to notice the dipping as with the maror, but not notice the making of the sandwich as a dipping. In that case, it still would be two.
The Gemara (Pesachim 115a) presents the celebrated dispute whether Matza and Maror must be eaten together or separately. The Chachamim believed that the Matza and Maror should be eaten separately and Hillel believed that the Matza and Maror should be eaten together. The dispute hinges upon how to interpret the Pasuk (Bemidbar 9:11) that states, "With Matzot and Maror should one eat it," whether the word "and" implies that the Matza and Maror must be eaten together. (We have merely presented a straightforward explanation of this dispute; a careful examination of Pesachim 115a, Tosafot ad. loc. s.v. Ella Amar Rav Ashi, and Rambam Hilchot Chametz Umatza 8:6-8 reveals more layers of interpretation, which we will not discuss in this essay.)
The Rishonim dispute whether Hillel would wrap the Korban Pesach together with the Matza and Maror (Rashi Pesachim 115a s.v. Shehaya and Rashbam ad. loc. s.v. Korchan) or eat the Korban Pesach separate from the Matza and Maror (Rambam Hilchot Chametz Umatza 8:6-7). This dispute accounts for the variations in the text of Zecher Lemikdash Kehillel that we recite before eating the Korech (see Baer Heitev 475:9 and Mishna Berurah 475:21). Some versions state, "He would wrap Matza and Maror and eat then together," in accordance with the Rambam's view. Other versions state, "He would wrap Pesach, Matza, and Maror and eat them together", following the view of Rashi and the Rashbam.
The Gemara concludes that since the dispute between Hillel and the Chachamim has not been resolved, we should accommodate both opinions. Hence, we should first recite the Berachot on Matza and eat the Matza, then bless on the Maror and eat it, and then eat the Matza and Maror together Zecher Lemikdash Kehillel (to remember the practice in the Beit Hamikdash according to Hillel). The Shulchan Aruch (Orach Chaim 475:1) codifies the Gemara's conclusion.
Let us ask another question to help address this one:
The question about the dipping is asked long before the Maror and Korech are dipped. So how is a child supposed to know to ask about why we have two dippings, if thus far there has only been one?
הביאו לפניו מצה. לפי שעקרו השלחן לפני מי שאומר הגדה ועושה הסדר קתני הביאו לפניו מצה ועקירת שלחן היא כדי שישאל הבן ואביו עונה לו עדיין יביאו שלחן לעשות טיבול שני והבן ישאל למה אנו מטבילין שתי פעמים ומיד כשעוקרין מחזירין לפניו והמצה והמרור עליו שהרי צריך לומר בהגדה מצה זו מרור זה וכדאמר לחם עוני שעונין עליו דברים הרבה
As explained by Tosafos, the table is removed from before the seder leader so that the child will ask. When the child asks about the removed table the father responds that they will bring the table back for the second dipping. This prompts the child to ask why we are dipping twice on this night.
According to this, the child is able to ask about two dippings even before the second one occurs because his father has told him that there will be a second one. Now if the entire question is based on this piece of information that his father tells him, there would be no reason for him to ask about a third dipping because he does not know that there will be a third dipping.