You're right, Oscar doesn't have a monopoly on badfic, far from it, I'm not familiar with the particular story you're talking about, do you have a link by any chance?
The most prolific badfic author I've ever seen was Hans Von Hozel. At one point he had well over a hundred short stories on his FFN profile, but at some point he got deleted. Many stories have however been salvaged by people who saved them and re-archived them in different places. Some stories are far worse for reasons other than mangled English. For instance, some of them have blatant Mary Sues (Like Jenna Silverblade, Ebony Dark'ness Dementia Raven Way....etc), where others have god awful subject matter (Like in Subjugation when Snape is a hermaphrodite who is repeatedly raped by Dumbledore and impregnated twice) and yet others are clearly written for shock value (Agony In Pink, Lunaticus....etc).
Usually, I think for a fic to qualify as a true badfic classic, I think that at least SOME of the following must be true:
1. It may be memorable years after it's release date
2. It may contain incoherence and/or gaping plotholes
3. It may contain terrible or non-existent grammar and/or spelling, making it hard to follow who is saying what, or even what is actually being said. (really, spellcheck is there for a reason)
4. It may be found squicky by the majority of people (like rapefic, scat...etc)
5. It may contain anatomically impossible/badly described sex scenes that leave the reader with unwanted mental images (like in the story Celebrian where she has a lavender labia)
6. It may contain far too much purple prose (for instance, detailed description of clothing, surroundings or physical appearance of characters that nobody cares about and isn't important tot he plot)
7. It may follow a plot which is incompatible with the fandom
8. It may be a crossover of two completely incompatible fandoms (for instance if someone tried to do a Harry Potter/South Park fic)
9. It may deviate too much from established canon without being labelled as an AU fic
10. The characters may be so far out of character as to be original characters with only the names in common with the canon characters.
11. The characters are put in a setting where they don't belong (like for instance, putting the crew of the Enterprise D in a high school as students)
Normally I's say that most classic badfics have three or more of these qualities, but it depends to what extent these qualities are exhibited it may be just one or two. It's something that's hard to judge sometimes if a fic is borderline, because I think everyone has slightly different yardsticks of how exactly they would define a classic badfic. Some though are so terrible that there appears to be a large degree of online consensus that a certain story is awful. With most of those I archive, there is an online consensus, although not with all, either because they didn't get enough attention initially to reach the same cult status, or simply because they faded to obscurity. For that reason I don't use infamy alone to judge it, but the other above factors too.