Antonym of "perfect, flawless" with the meaning that *everything* is faulty
Example:
Peter got a perfect/flawless/impeccable score: 0 errors for 100 questions.
John got a ? score: 100 errors for 100 questions (Yes, he filled out the questions. And probably smudged with the extra benefit of grammatical and spelling errors in hen scratching).
The problem with "normal" antonyms is that they fit a range of results. The words "worst possible" or "best possible" are sounding more than statements than judgements. "Perfect"/"Impeccable" contains the information that it not only contains no errors, it gives the impression that it should not contain errors.
The searched word should immediately inform the reader that if something is measured on a scale, this result is the worst possible result. Beyond fubar. We hit the rock bottom. A perfect screw-up.
EDIT: If there is no such word and I am stuck with "worst possible", that would be nice to know, too. But I must admit, the "unworsenable score" has something...
Solution 1:
I suggest nadir.
TheFreeDictionary defines this as (which includes the phrase "rock bottom" that you used):
bottom, depths, lowest point, rock bottom, all-time low
Merriam-Webster defines this as:
the worst or lowest point of something
Dictionary.com defines this as:
the lowest point; point of greatest adversity or despair.
There are examples out there of the phrase "nadir score" being used to indicate the lowest score on a scale. Here is one example:
the IMI-C nadir score (the lowest scale score obtained by a particular patient)
Solution 2:
The word abysmal is an extreme adjective (though perhaps has lost force because it is used in unmerited (!) situations). Acording to Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc it means
adj.
of or like an abyss; immeasurably deep or great: abysmal ignorance.
extremely or hopelessly bad or severe: abysmal weather.