Eighteen months ago we had an anomalous problem where video playback didn’t work on some, but not all, of our WordPress multisites. Videos wouldn’t play, or would play but wouldn’t seek. The problem was confined to local uploads embedded in a page. Videos from YouTube played fine; if you viewed the video directly playback worked as expected.
The problem turned out to be long-standing issue with how ms-files.php served up files from pre-WordPress 3.5 multisites. Solutions had floated around for years. Our problem was describing the problem with enough specificity to actually find the right solution.