The text of minor illusion specifies it creates the "image of an object", but one of the examples is plural ("muddy footprints"). Can it create multiple objects as long as they fit within a 5' cube?
If yes, does touching one of the objects reveal the others as illusions? (imagine trying to hide a real object among many illusionary duplicates)
Per What is considered an object? , the definition of object is on pg 246 of the DMG:
...a discrete, inanimate item like a window, door, sword, book, table, chair, or stone, not a building or a vehicle that is composed of many other objects.
And yet a window is composed of glass, wood, metal fixtures, etc.
Contradictions in terms (which "What is an object?" invariably boils down to - see also Do liquid items stay separate in a Bag of Holding?) are the DM's jurisdiction.
@Jack mentions the spell seems to offer guidance on what counts as a single "thing":
such as a chair, muddy footprints, or a small chest
... so there's a case to be made for a bookshelf full of books, or a plate full of food, or something similar.
From minor illusion:
Physical interaction with the image reveals it to be an illusion, because things can pass through it.
So a shopkeeper or a guard could just pass their hand over every illusion and detect the correct one, for example.
Minor illusion says:
If you create an image of an object--such as a chair, muddy footprints, or a small chest--it must be no larger than a 5-foot cube
You are reading this and thinking, multiple footprints aren't really one object, are they? And no, they are not. But the spell also seems to contradict itself about the number of sounds you can make - it says (emphasis mine):
You create a sound or an image of an object within range that lasts for the duration.
but then says:
The sound continues unabated throughout the duration, or you can make discrete sounds at different times before the spell ends.
So can it make just one sound, or multiple sounds? Can it make just one muddy footprint or multiple footprints?
RAW is unclear, because of the vague and contradictory wording of the spell. I recommend that you think of it in terms of the spell being able to make one illusion. Since the spell doesn't actually make objects, merely images, don't try to restrict it to things that meet the rules definition of objects. It should be able to make an image of a pool of water, for example, even if the rules don't classify liquids as objects.
'One illusion' is a conceptual or memetic unit, not a physical one. The theme of the illusion should be able to be expressed simply in the way that the examples given are - either a noun (a chair) or, at most, an adjective and noun (your voice, someone else's voice, a lion's roar, a beating of drums, muddy footprints, a small chest). Anything more elaborate should be beyond the power of the cantrip. In this sense, "a sword and a shield" is two illusions and would not be allowed - but "muddy footprints" is one illusion, because it is one concept. A "lion's roar", repeated over and over again for a minute, is one illusion. A "lion's roar followed by your voice" is two illusions, and should not be permitted.
Can it create multiple objects as long as they fit within a 5' cube?
It can create an image of multiple copies of the same thing: muddy footprints. It cannot create different things: a sword and a shield.
Does touching one of the objects reveal the others as illusions? (imagine trying to hide a real object among many illusionary duplicates)
Since it is one illusion, touching any part of the image reveals the entirety of the image as illusory:
If a creature discerns the illusion for what it is, the illusion becomes faint to the creature.
If there was one real muddy footprint, surrounded by dozens of illusory ones, your successful Investigation of any of the illusory ones would render them all faint (since they are all the same illusion), making the single real one stand out.
