One of Moshe's greatest traits was his strong connection to Am Yisrael. Even though he was brought up in Pharaoh's palace, he identified strongly with the Jewish people, and went so far as to kill an Egyptian who was beating a Jewish slave. 
Moshe strongly identified with the Jewish people.
However, sometimes it is the small actions that are even greater tests. Running into a burning house to save a child is externally a truly great act deserving much commendation. However, most people would do that in those circumstances. On the other hand, whether or not a person refrains from speaking badly about other people might have much more internal meaning and be a better indication of the true state of a person's being, and to what degree they care about other people. Although, the intention here is definitely not to state that Moshe's killing of the Egyptian was an equivalent test to running into a burning house to save somebody. Far from it; rather, the idea is that small actions can often have more internal implication than great external actions.
Moshe strongly identified with the Jewish people. But did he identify so strongly with them that he felt great pride in being part of Am Yisrael and cherished his identity as a part of them so much that once he was freed from Pharaoh's palace he would desire for it to be clear that he was one of them, and would he immediately correct any false impressions that he was representing the Mitzrim? Or had the fact that he was forced to hide his identity when in Pharaoh's palace, in Galut, crept inwards and had a real effect inside, on his pride in being part of Am Yisrael and on his pride in their heritage?
Furthermore, had his constantly seeing Bnei Yisrael in their most degraded state in history caused Moshe to loose some of his pride in Am Yisrael? Or would Moshe be able to maintain his self-worth and the pride in his people and his people's heritage, as Yaakov Avinu did when he approached Esav, bowing seven times, yet maintaining within the full knowledge that Esav was only temporarily experiencing external exaltation and that the true pride, self-worth and honor of the people of Avraham, Yitzchak and Yaakov would never be extinguished, and would exist forever, even if it would at times be hidden within?
Yaakov's situation was different. Moshe saw the people's degradation and was affected by it. He was affected by the pressure of the general outlook on the "Jew" in Galut. Both the outlook on his people by the Mitzrim and even by themselves. His connection to Am Yisrael was strong, but his pride in his people, and his feeling of their great worth, was lessened by the harsh external reality in Galut. His connection to Am Yisrael was weakened. To the degree that a person takes great pride in Am Yisrael and understands deeply their true worth and segula, despite unfavorable external layers, to that degree he will have an even greater connection to Am Yisrael, in the midst of their deprivations.
Moshe's sense of pride in his people and his heritage had been lessened by his time in Pharaoh's palace. Once released from there, it did not shine forth and express itself in a desire to be identified as one of Am Yisrael and not as a representative of the nation that Am Yisrael had found itself within in Galut.
This was not just the fault of Moshe. It was the fault of the whole generation. They had all been affected by Galut. They had lost their strong connection to their heritage, to their forefathers and to the land that HaShem had promised to them. But if Moshe had managed to be an example in this area, to shine forth in his pride in being part of Am Yisrael, and in Am Yisrael themselves, in the understanding of their true worth, with a strong connection to the roots of Am Yisrael, the Avot, with the strong desire to see the promise that was made to the Avot fulfilled, then perhaps Moshe could have brought the whole people along this path with him. Then, they would have been able to enter Eretz Yisrael immediately, together, without the forty years wandering in the desert, and it would have been the start of the messianic era.
All the mistakes that happened were a result of the erosion that Galut had on the identity of Am Yisrael. If Moshe had had a stronger connection to that identity, he would not have allowed himself to be presented as a Mitzri to Yitro's daughter; he would have had a greater sense of the segula, the priceless treasure that is a Jewish soul, and in the worth of Am Yisrael. He would not have protested to HaShem at the burning bush that Bnei Yisrael would not listen to him.
Why did HaShem need Moshe to react to the announcement of his mission, before HaShem gave Moshe the 
They had all been affected by Galut. They had lost their strong connection to their heritage.
signs? Because if Moshe had not felt that he needed to ask, and instead had burned with pride in his people, their ancestry, their true worth and their heritage, and their importance to the fulfillment of HaShem's purpose for mankind in history, then Moshe's exuberance and radiating pride and trust in the people would have convinced the Jewish people, and brought them along with him, out of the depths of their affliction in Galut.
If Moshe had been at this level, then he would have been more connected to the Jewish people, and would have had an even greater understanding of them. He would not have become angered at them and struck the rock. He would have thought clearly and acted according to the command of HaShem. He would have understood where they were coming from, and known that they did not need rebuke at that time; and that HaShem's intention was to teach them in a gentle manner, through the example of the rock: just as a rock was receptive to a spoken order from HaShem, they too should be attentive and fulfill G-d's word.
However, as said above, this did not just affect Moshe. Aharon also was affected by this. If Aharon had had more confidence in the people, he would have stopped them from making the golden calf. He would not have feared that they would not listen, and that they would instead make the calf even sooner, and might even kill him. Rather, he would have had an even stronger connection to the Jewish people, he would have believed in them more, and them in him, and he would have stopped them.
The Jewish people were responsible for Chet HaMeraglim. They definitely were affected by Galut and the weakening of their connection to their identity as Am Yisrael, and their connection to Avraham, Yitzchak and Yaakov, and their identification with them, their lives and the promise of HaShem to them, was part of the reason for Chet HaMeraglim. Had they had a greater connection to the Avot, they would have learned from the war that Avraham fought against the five kings, and they would not have been as afraid of the inhabitants of Canaan. Had they had a greater connection to the Avot, they would have had a greater desire to live in the land that the Avot lived in, the land that was promised to Am Yisrael by HaShem as an inheritance. Had they had a greater connection to their identity as Bnei Yisrael and had great pride in it, then they would not have seen themselves as grasshoppers, but as warriors for HaShem, His Torah and His people. Then again, if Moshe and Aharon had managed to maintain a greater sense of pride and of the worth of the Jewish people and their heritage, then maybe they would have been able to re-infuse Am Yisrael with it.
But it is impossible to allot responsibility and blame. Only HaShem is capable of that. The interplay between all the different parts is less like a two-sided scale than like a thousand scales, all tied by ropes and pulleys in different ways to one another, such that if you place a weight on one, it affects some others, and if you lift one, it has implications on the others. However, one thing is clear. The essence of the problems of the Jewish people in Galut is their lack of feeling the great worth and importance of being part of Am Yisrael. The essence of these problems comes from a lack of feeling great pride in the Jewish people and their heritage, in their ancestors, their Torah, their land and their historic mission. The essence of these problems comes from a lack of being connected to these things, and a lack of being connected to and sensing the immense worth of every other person in Am Yisrael.