Ch. 20, v. 11: "Va'yach es ha'sela" - And he smote the stone - Rashi in the following verse explains that Moshe did not maximize the "kiddush HaShem" because had he only spoken to the stone the masses would have learned a more powerful message of hearkening to HaShem. If a stone, which awaits no reward or punishment follows HaShem's WORD, all the more we should follow HaShem's commands. This is a bit difficult to understand. The stone's miraculously giving forth water in response to being hit with a staff conveys the same message. What difference is there if the mode of communication is "talking to a rock" or hitting it?
Rabbi Moshe Feinstein in Dorash Moshe explains that we could have learned the message that our WORDS have a positive effect when we attempt to bring someone closer to proper Torah observance, even when we feel we are "talking to a rock." This lesson is not derived from smiting the rock.
Perhaps there is another symbolism here as well. The Torah is likened to water. The first time, Moshe hit the rock and it issued forth water. Now he was to speak to it. Issuing forth water, studying and understanding Torah comes with difficulty, symbolized by smiting. When one continues studying, understanding comes more easily, just as speaking is a lesser effort than smiting.
Ch. 20, v. 12: "Lo he'emantem" - You have not caused faith - The Yalkut Shimoni says that there were four misdeeds. Our verse says "lo he'emantem," meaning that HaShem commanded that Moshe talk to the rock, and instead he smote it, "lo kidashtem" (Dvorim 32:51), meaning that they did not bring forth water from any stone that was requested of them, "m'altem" (ad loc.), meaning that Moshe told them off by saying "hamin ha'sela" (verse 10), and "m'ri'sem" (verse 24), meaning that they did not speak in front of the rock, i.e. they did not teach a chapter of Torah knowledge.
Ch. 20, v. 8: "V'dibartem el ha'sela l'ei'nei'hem" - And you shall speak towards the stone in front of their eyes - What should Moshe say? The M.R. 19:9 says that he was commanded to say a halachic dissertation. The N'tzi"v offers 2 explanations of this Medrash. One is that with Moshe's telling over words of Torah to all of the bnei Yisrael he would re-enact the giving of the Torah at Har Sinai, as the words that would emanate from his throat would be on the level of HaShem Himself communicating. When the giving of the Torah took place there was a supernatural flow of water, as related in Shoftim 5:5, "af ovim notfu mayim." Here too, this activity would bring about an abundant flow of water. Alternatively, he offers that anytime there is a congregation of bnei Yisrael learning the Torah it creates a Celestial influence of happenings that are not restricted by nature, so water would abundantly flow even from a dry rock in the middle of the desert.
Ch. 20, v. 11: "Va'yach es ha'sela b'ma'teihu PAAMOYIM" - And he smote the rock with his staff PAAMOYIM - We are accustomed to translate PAAMOYIM as twice. Why would Moshe strike the rock twice? The M.R. says that when he struck the rock the first time only a trickle of water came out. Upon striking it a second time it emitted a powerful stream. However, the Mechilta of Rashb"i writes on the word PAAMOYIM, "chad d'ovid hashto v'chad d'ovid mikodem," - one that he did now, and one that he previously did. It seems that according to this interpretation, PAAMOYIM does not mean TWICE, but rather, a second time. Moshe had already struck the rock earlier, as recorded in Shmos 17:6. (Haksav V'hakaboloh)
Ch. 20, v. 10: "Shimu noh hamorim" - Because Moshe spoke in a harsh manner, he created an atmosphere of toughness. He could no longer speak softly to the rock to give forth its waters. He now had to hit it. His shortcoming was in his manner of speech, not in the actual hitting, as it was only a result of his previous action. (Kedushas Levi)