The reason why the first example does not use an article while the two others do is because the first does not refer to a specific amount.
If instead of an unspecific number of minutes you were to say it crashed in ten minutes then you would instead write:
The plane crashed a mere ten minutes after take-off.
On the other hand, if we were to rephrase the other examples so that they do not refer to specific quantities then we could drop the "a":
It cost mere cents. (I changed dollars to cents, because though
grammatically correct either way, cents sounds a lot better in this
The city receives mere percentage points of the parking revenues.
In a sense, you are wrong when you say dollars and 20% are plural nouns. In these usages, they are effectively being treated as if they were singular. The "mere" is not qualifying the items in the set individually as would be the case in the phrase "the boys are hungry", but the set as a whole. It is the 20 dollars as a collective unit that is mere. The case is not that each individual dollar is mere and there simply happens to be 20 of them.
To reveal this fact further, consider the grammatically correct phrase:
He quit his job after a mere 2 day period.
He quit his job after mere days.
He quit his job after a mere 2 days.
As you can see both the "a mere 2 day period" and "a mere 2 days" are treated the same way. This is because they are both referring to a 2 day chunk of time. A chunk of time that is taken as a whole and said to be meager.