I am wondering if this is in reference to a 1998 horror film where the protagonists escaped. Is there a particular movie being referenced? Or am I at this point just looking for Easter Eggs where there are none?
TV Tropes says:
It's mentioned that the American facility has only failed to complete its ritual once before, in 1998, due to a screw-up by the Chem Department. Was that date chosen at random, or was a movie released that year that Joss Whedon thought was exceptionally-lame, even for schlock horror?
The best explanation seems to be The Faculty, since it had no fatalities except [see spoiler below], and it makes sense with the chem department part:
Scoping a list of 1998 horror films, the only one that sticks out is The Faculty. There isn't a single fatality within the main cast of students (save for the "Virgin" who is ultimately revealed as the monster). And to make matters worse the monster's undoing turns out to be the stoner's custom mix. Damn chem department indeed...
The 1998 glitch is a reference to The Faculty. The film has all five archetypes (fool = Clea DuVall, jock = the ginger guy, whore = Delilah, scholar = Josh Hartnett [some might argue he is the fool, but he is not if you've seen more than 10 minutes of the movie], virgin = Elijah Wood). None of the five archetypes die. The monster (alien) is killed by a home-made narcotic amphetamine cooked up by the Scholar (aka the Chem Department's fault). Hope this helps.
I reviewed the 365 movies listed as horror movies from 1989 on IMDB, and nothing jumps out...there are a number of horror sequels which were part of a big franchise, but nothing which I would regard as iconic. If I were aiming to reference a movie, I'd be inclined to reference Evil Dead I or II, but those are 1981 and 1987 respectively.
It is interesting to note, however, that 1989 is when Joss Whedon started working on Roseanne. It may be a hat-tip to his first big job.
The "1998 almost-disaster" could refer to The Faculty or The Cabin, but I believe it refers to the infamous monster which rocked New York in 1998, ???zilla. The film "Godzilla 1998" was disavowed by the Japanese, hated by Americans and Europeans, panned as bad worldwide. Veteran actors & directors of original Godzilla movies mocked the look of ???zilla. Nakajima stated that 1998 ???zilla looked "like an iguana and its body and limbs look like a frog". One of the recent Godzilla films have referred to "98 ??Zilla" as "The New York Incident", so in conclusion, when Lin, Sitterson and Hadley are discussing the "1998 almost-disaster", they are indeed referring to the monster that briefly got away...
There was a movie from 1998 called simply The Cabin.
Six teenagers go up to an old cabin in the woods for a vacation get-away. When they get there, strange things start happening. The cabin was used as a torture/execution site in medieval times. A young man named Jared, who was convicted of killing his wife, was tortured to death. Only thing was, he was innocent, and his soul is now trapped in that very cabin. His soul can't be released until the cabin is destroyed. Jared placed a spell on Earth, in the year 1998 AD, to make Earth devoid of light and life. One by one, the kids are turned into bloodthirsty, merciless zombie-deadites, as Jared possesses their very bodies, in an attempt to make them destroy the cabin. The helpless kids fight for their very lives against what used to be friends and lovers.
It was pretty similar to Cabin in the Woods.