Is there a term that describes the class of words that, if accidentally dropped, completely invert the meaning of the sentence?

Solution 1:

There are really two concepts at play here. The first is logical negation:

In logic, negation, also called logical complement, is an operation that essentially takes a proposition p to another proposition "not p", written ¬p, which is interpreted intuitively as being true when p is false and false when p is true.

So what you define as "invert the meaning" is logical negation and is possible whenever negation is added or removed from a sentence. This covers two of your examples:

Dropping not: "The 1930s were not Germany's finest political period" becomes "The 1930s were ... Germany's finest political period".

Dropping just: "Designing space-age rockets was not just hard; it was cool" becomes "Designing space-age rockets was not ... hard; it was cool".

The latter is an issue of "just" moving the negation from "just" to "hard". The problem word is still not; it isn't just.

Other examples of this sort are adding or removing "un" or "a" from the beginning of a word:

I have been incredibly (un)kind.

How (a)typical!

The third example is really not the same kind of problem as your first two examples.

Dropping if: "If the briefcase is his, you will execute the spy" becomes "... The briefcase is his, you will execute the spy".

Dropping if doesn't invert the meaning of the sentence in the same way. Inverting the sentence using negation would be either:

If the briefcase is his, you will not execute the spy.

If the briefcase is not his, you will execute the spy.

Which means that we need a different type of classification. In this case, the problem is due to removing a conditional and turning the result into a non-conditional command. Other mistakes of the same kind:

I looked at Alice and said, "Bob, kiss me!"

I looked at Alice and said, "Kiss me!"

From Wikipedia:

Conditional sentences are sentences expressing factual implications, or hypothetical situations and their consequences. They are so called because the validity of the main clause of the sentence is conditional on the existence of certain circumstances, which may be expressed in a dependent clause or may be understood from the context.

If you remove the conditional part of the sentence the whole meaning changes -- or in your words, inverts.