I will join in here, several months later. While I build sites for clients, I don't currently have any videos on client sites. However, on my own business site, I have three videos. These three rendered smoothly, play back smoothly on any device, and are absolutely normal in every way - until I upload them to my SQSP site. Every single one has an audio/visual glitch at the two-minute mark. This is present in videos uploaded today, and videos uploaded six months ago.
Squarespace has something going on with their video service, and I'd sure love to know what it is. As a video guy, this is driving me nuts.