There's a song I've been practicing since forever. It's above my skill level, but I've been improving nonetheless.

I've read very often here that if a song is giving you fits, slow it down, and use a metronome.

So, I've taken a song that's 120 beats per minute, and I'm playing it at 80. I can't believe how much I'm screwing it up, far more than if I try to play 100 or more.

Is it normal to mess up at first when really slowing down the pace? It's also the first time I've used a metronome with this song (just this song), which is distracting.
Yes, it's a matter of coordination between your picking and fretting hand. When you play at the higher tempos you dont notice as much because you are concentrating on trying to play all the notes, but when you slow down you pay more attention to what you are playing and hear all the sloppy/misfretted notes. If you can improve that it will help you a lot when you play it at normal speed.
I agree that it's generally the case and should be evidence of technique issue, but I don't think this is uncommon even with good players when they slow it down, possibly to speeds they're not used to playing.

I couldn't help thinking about this while reading the thread.
Haven't you seen some great guitarist on youtube demonstrating "How to play the main riff from [insert difficult song here]" - then first they play it full speed flawlessly with seemingly no effort. Then they go "And here is the same thing at a much slower tempo. Oops...oh wait that's just wrong... damn this part is hard to play slow". And they keep messing up, then change speed and it's beast mode again.
Thats likely because when you get used to playing something at a high tempo your fingers move by muscle memory and when you play the same thing at a slower tempo it feels completely different and you have to think about position shifts and picking patterns, thats why the guitarists you mention go "what the hell am I doing?".

Most likely the issue TS is having is just coordination between fretting hand and picking hand. That and the fact that at a slower tempo it is very easy to hear the sloppyness you would not hear at full speed.
That's what happens if you don't actually know the rhythms or notes thoroughly.

It's like imitating someone speaking a language you don't know. You might be able to imitate a sentence at full speed by approximating the sounds, but unless you know the actual words, you wouldn't be able to say each syllable individually.