One group of users reported that iOS 9 upgrade would fail after several minutes, requiring them to start the process over. Many posted screen shots of the error message they received: "Software Update Failed".
That problem could be caused by servers that were overloaded when too many people tried to download the upgrade simultaneously.
Other users, many of them with older devices, reported their devices seizing up on a "swipe to upgrade" page. The latest upgrade had been deemed by Apple as "friendly" to the older devices after the iOS 8 problems.
Apple has not yet officially commented on the issues.
The release of the previous version of the iOS (iOS8) was also problematic in the beggining, and Apple had released several further updates since then, although some of the bugs were never fully fixed.