In what way did the Israelites complain against God in the wilderness?

Summary

1. The Israelites complained about misfortunes, food, drink, the allocation of the priesthood and Moses
2. In spite of all the miraculous signs they had seen they refused to believe (Num 14:11)
3. Their complaint sometimes included the accusation that God had brought them into the wilderness to kill them. 
   1. This demonstrated extreme ingratitude since God had not long before delivery them slavery and from the Egyptian army.
4. They blamed Moses and God for the present difficulty.

They complained about their misfortunes

Num 11:1 ESV  And the people complained in the hearing of the LORD about their misfortunes, and when the LORD heard it, his anger was kindled, and the fire of the LORD burned among them and consumed some outlying parts of the camp.

They complained about their that the land was dangerous and they feared death

Num 13:32 ESV  So they brought to the people of Israel a bad report of the land that they had spied out, saying, “The land, through which we have gone to spy it out, is a land that devours its inhabitants, and all the people that we saw in it are of great height.
Num 14:1-3 ESV  Then all the congregation raised a loud cry, and the people wept that night.  2  And all the people of Israel grumbled against Moses and Aaron. The whole congregation said to them, “Would that we had died in the land of Egypt! Or would that we had died in this wilderness!  3  Why is the LORD bringing us into this land, to fall by the sword? Our wives and our little ones will become a prey. Would it not be better for us to go back to Egypt?”

Num 14:11-12 ESV  And the LORD said to Moses, “How long will this people despise me? And how long will they not believe in me, in spite of all the signs that I have done among them?  12  I will strike them with the pestilence and disinherit them, and I will make of you a nation greater and mightier than they.”

Num 14:26-27 ESV  And the LORD spoke to Moses and to Aaron, saying,  27  “How long shall this wicked congregation grumble against me? I have heard the grumblings of the people of Israel, which they grumble against me.

They complained that the food was unsatisfying 

Exo 16:2-3 ESV  And the whole congregation of the people of Israel grumbled against Moses and Aaron in the wilderness,  3  and the people of Israel said to them, “Would that we had died by the hand of the LORD in the land of Egypt, when we sat by the meat pots and ate bread to the full, for you have brought us out into this wilderness to kill this whole assembly with hunger.”
Exo 16:12 ESV  “I have heard the grumbling of the people of Israel. Say to them, ‘At twilight you shall eat meat, and in the morning you shall be filled with bread. Then you shall know that I am the LORD your God.’”

They complained about Insufficient water

Exo 17:2-3 ESV  Therefore the people quarreled with Moses and said, “Give us water to drink.” And Moses said to them, “Why do you quarrel with me? Why do you test the LORD?”  3  But the people thirsted there for water, and the people grumbled against Moses and said, “Why did you bring us up out of Egypt, to kill us and our children and our livestock with thirst?”

They complained that they wanted the priesthood

Num 16:3 ESV  They assembled themselves together against Moses and against Aaron and said to them, “You have gone too far! For all in the congregation are holy, every one of them, and the LORD is among them. Why then do you exalt yourselves above the assembly of the LORD?”
Num 16:4-5 ESV  When Moses heard it, he fell on his face,  5  and he said to Korah and all his company, “In the morning the LORD will show who is his, and who is holy, and will bring him near to him. The one whom he chooses he will bring near to him.
Num 16:20-21 ESV  And the LORD spoke to Moses and to Aaron, saying,  21  “Separate yourselves from among this congregation, that I may consume them in a moment.”

They complained that Moses killed the people

Num 16:41 ESV  But on the next day all the congregation of the people of Israel grumbled against Moses and against Aaron, saying, “You have killed the people of the LORD.”
Num 16:43-46 ESV  And Moses and Aaron came to the front of the tent of meeting,  44  and the LORD spoke to Moses, saying,  45  “Get away from the midst of this congregation, that I may consume them in a moment.” And they fell on their faces.  46  And Moses said to Aaron, “Take your censer, and put fire on it from off the altar and lay incense on it and carry it quickly to the congregation and make atonement for them, for wrath has gone out from the LORD; the plague has begun.”
Num 16:49 ESV  Now those who died in the plague were 14,700, besides those who died in the affair of Korah.