An oversight of oversight
Having oversight of something means you’re in charge of it, or managing it. It’s a pretty old word, and has been used to mean some form of authority or supervision for centuries. Queen Margaret of Anjou used “oversight” in this way in a letter from about 1421: “Send sum trusty man for to go with hem, that may have the oversighte & gouveurnance of hem alle.”
“Oversight,” at least in this case, is derived from “oversee,” which means much the same thing and is even older, coming from Old English. Even older versions of the word can be found in various ancient Germanic languages. It’s still in common use today; in many hierarchical organizations (such as a large company or a government), a department or committee is described as “having oversight” over some area of activity or budget.
Doubtless due to some historical oversight, “oversight” also means to FAIL to see or notice something. This sense of the word has been there since the beginning; in Richard Mulcaster’s 1582 textbook about writing English, he included this: “Whereby it appeareth, that no consonant can be dubled in the end of a word..: and that therefor the dubling of the last syllab is mere ouersight.” Even the pairing “mere oversight” is still common today, centuries later.
So “oversight” means both scrutinizing something and failing to even notice it. That makes it a somewhat unusual thing in English: a “contranym” — a word that means the opposite of what it means. Contranyms are rare in terms of the number of words in English, but they’re not at all rare in use. “Oversight” is commonly used. So is “sanction”, which means both “give official approval” and “penalize.” The National Football League, for example, previously tacitly sanctioned players kneeling during the national anthem, but later they announced that such acts will be sanctioned.
Or how about an even more common word: “dust,” which (especially in its gerund form “dusting”) means to remove dust (when it’s the kind you don’t want) and to apply dust (when it’s the kind you do want, like if you’re a detective looking for fingerprints). “Seed” is like that too; if what you’re seeding is your lawn you’re adding seeds, and if what you’re seeding is a tomato, you’re removing them.
There are other contranyms in English. If you stop holding fast to your preconceptions, and think fast, you’ll probably think of some! I’d suggest you clip out possible entries from books and magazines, then clip together the best ones. You’ll have to stop if the lights go out, unless of course the sun is out at the time.