Moshe said to them: "Let no person leave of it till the morning.' But they did not obey Moshe, and some of them left of it until the morning, and it bred worms, and rotted. (16:19-20)
Why did the manna have to spoil each morning? One reason is obvious. The manna was supplied was not just to keep the Jews from starving, but also to train them to depend on God: "[Hashem] fed you the manna, which you and your fathers did not know of, to show you that man does not live by bread alone, but by the decree of Hashem" (Devarim 8:3). Every morning the Jews woke up with an empty pantry and nothing to rely on but the promise that God would provide them with more food.
I think there is another possible reason, which we see by comparison to a completely different topic - korbanot.
For those Temple sacrifices which are eaten by human beings (as opposed to being burnt on the altar), the eating must be done within a certain period of time (see Zevachim chapter 5). For a few sacrifices, this period is two days and one night (i.e. the remainder of the day on which it is sacrificed, plus 24 hours, until sundown). For all other sacrifices, the period is one day and one night. This means that the sacrifice must be entirely consumed by daybreak after it is sacrificed. The Torah warns us a number of times not to leave sacrificial meat "until morning" - in Shemot 12:10, Vayikra 7:16 and 22:30, Bamidbar 9:12, and Devarim 16:4, regarding different types of sacrifice.
Just as sacrifices must be eaten by morning, so too manna, and perhaps this hints at a deeper similarity between them.
A second similarity between manna and sacrifices appears if we look at Shabbat. As we know, a double portion of manna fell before Shabbat and none on Shabbat. (This is commemorated in our modern double challah bread on Shabbat.) Similarly, the Shabbat musaf offering is virtually identical to the daily tamid offering - two sheep and two tenth-eifah mincha offerings. This means that overall, double as many sacrifices are offered on Shabbat as on weekdays. This double sacrifice is parallel to the double manna associated with Shabbat.
A third commonality between manna and sacrifices is the focus of their location. A jug of manna was to be placed "before Hashem, as a remembrance, for your generations", next to the ark in the Mishkan (Shemot 16:33). This parallels the many sacrifices which were to be brought "before Hashem" in the Temple, and especially the lechem hapanim, another kind of bread which was to be placed "before Me, forever" (Shemot 25:30)
The upshot of all of this is that it's possible to see the eating of manna as a parallel to the eating of sacrifices. Perhaps living in the desert was like a perpetual visit to the Temple, and eating the desert food was like a perpetual sacrificial occasion.
Moshe built an altar, and named it Hashem-Nissi. And he said: "A hand upon the throne of Hashem: there will be war to Hashem with Amalek from generation to generation." (17:15-16)
Two questions arise when reading the lines. 1) Who is "he" who spoke, Moshe or God? 2) What does the phrase "a hand upon the throne of Hashem" mean?
All the standard commentators say that the raising of a hand indicates the making of an oath, and so God is promising that He will wage war against Amalek. I agree that an oath is being made here. But I would like to suggest that perhaps it is Moshe, not God, who is speaking and making that oath.
There is one other occasion in the Torah when someone places their hand on a chair:
"Avraham said to his servant, the elder of his house, who ruled over all that he had: 'Please place your hand under my thigh.' " (Breishit 24:2)
When a person is standing, there is no "underneath" their thigh. So Avraham must have been sitting at the time. He asked his servant to place a hand between Avraham's thigh and the chair, below the thigh and above the chair. This is exactly the gesture we have in Shemot - a hand is placed on a chair (or throne).
Who made the oath in Breishit? The servant, who swore to his master Avraham that he would not marry Yitzchak to a Canaanite. The physical gesture of a hand under the thigh is suggestive of the servant-master relationship: to put your hand in such a position, you must crouch or bow down, making yourself literally subordinate to your master, reflecting your social role. You accept the master's authority over you, and the promises you make to the master become binding commitments you must fulfill.
(This is the pshat, while the midrash says that the servant held Avraham's brit milah. This is a very perceptive interpretation. It highlights the oath and the role of Yitzchak both regarding brit milah and here: there God says that the covenant will be perpetuated through Yitzchak; here Avraham moves to ensure that Yitzchak's role in the covenant is upheld. The ideas of brit milah were probably on Avraham's mind when he beswore his servant - that's what we can learn from the midrash. But we should not think that the servant's hand was literally on Avraham's brit milah, since we have a good explanation that does not require adding extra details to the story.)
In Shemot, we have the same gesture of a hand being placed on a chair (metaphorically, since God and His throne are not physical), and I would like to interpret it the same way. Clearly God is the master and Moshe is the subordinate. That means Moshe, not God, is making the oath! Why does Moshe do this? He has just been saved by God from the attacking Amalekites, and like any good Biblical figure who has just been saved, he builds an altar and swears loyalty to God from then on.
What about the contents of the oath? The phrase "milchama lahashem ba'amalek" is normally translated as "God will be at war against Amalek", indicating that God made the oath. Were we to take the phrase in a vacuum, I think this would be the simplest meaning, and this also has the best continuity with the previous verse.
I have two responses to this claim: 1) The phrase "milchama lahashem ba'amalek" could be translated as "There will be a war dedicated to God (=a holy war) against Amalek", with the war conducted by Israel. 2) Moshe could be pledging his loyalty to God, as a response to the promise God just made regarding Amalek.
Given how confident I am about the throne metaphor, I think one of these two approaches is preferable, even they make the phrase "milchama lahashem ba'amalek" seem more awkward in isolation.
What about the identity of the speaker in the phrase "And he said"? This phrase too is ambiguous. The commentators would say that "he" refers to Hashem from "Hashem-Nissi" in the previous verse, even though this is a proper noun and Hashem doesn't do anything active in that verse. Whereas I would say that since the previous verse spoke of Moshe building an altar, this verse speaks of Moshe making an oath.