The "Detect Thoughts" spell has as its material component "a copper piece". (Yet another in the long list of punny material components.) The rules for material components say,
Casting some spells requires particular objects, specified in parentheses in the component entry. A character can use a component pouch or a spellcasting focus (found in “Equipment”) in place of the components specified for a spell. But if a cost is indicated for a component, a character must have that specific component before he or she can cast the spell.
Does requiring "a copper piece" mean that a "cost is indicated" and so it requires one to actually be holding a coin, rather than just using a spellcasting focus or component pouch?
Usually a cost being indicated is worded like "something worth at least 25 gp", so since this isn't phrased as "a copper piece worth 1 cp" or even "a one-cp coin", I'm not sure that it means that a "cost is indicated". It seems to more just be describing a random object associated with the spell like other "normal" spell material components. But then again, I can see a good argument that a coin used for currency would be the most straightforward way of indicating a cost that there is.
Obviously in general adventurers won't usually have a lot of trouble finding a copper piece during their travels, but I could imagine some circumstances where it would be inconvenient for a spellcaster to need to dig a coin out of their pouch while their spellcasting focus is already in hand.
Best Answer
"Penny for Your Thoughts"
Although the writers were almost certainly referring to a common copper coin for their joke, there's no indication this was meant as an actual "cost". The 5e authors consistently use the term "worth" or "value" whenever an actual material component cost is indicated, and they express that cost in gp (I've yet to find one costing less than 5 gp).
Copper pieces are so low in value that I don't believe anyone would consider them a real "cost" (even if it was say, 11 copper pieces to cast Gentle Repose on a Beholder). They're less valuable and far easier to find than most cost-free material components.
I wouldn't spend much time worrying about it.... but that's just my 2 cp.