For me it was a DirectX issue. Specifically DirectSound. It happened after I upgraded from DirectX 5 (what FF7 comes with) to 7. Along with getting stuck at Cosmo Canyon, certain sounds in the game developed a 2-second delay. Plus, they became reverb happy. I manually downgraded to 5 again (rebooted in MS-DOS and copied+overwrote all of the files in the DirectX 7 folder with the ones from the FF7 install cd.) and it went away.
According to Eidos' tech support, the problem is that for some (unknown) reason the game doesn't load the next video in the scene. So you're probably looking for the right needle, Threesixty.
As a rather useless aside, the interesting thing was that, when I was having these problems, it turned out that there was a way I could get around it. Part of it was that the first time I played through the game I didn't find Gongaga and just went right by it without knowing it was there. Then, I also went by Cosmo Canyon without noticing it. =P The thing is,
the Buggy didn't break down like it was supposed to. I got to the river before realizing, "...wait a minute. Was that a bulding back there?" It was very odd to meet a guy inside who said he'd fix my buggy when it wasn't even broken... I guess that just goes to show, though. I'm not exactly Mr. Observant, missing two whole locations like that.