While using the rich-text editor, some of them noticed that the most recent line of previously entered would disappear suddenly, much as described in this bug report. However, they also report that it doesn't always happen after a backspace: in a couple cases hitting Enter does it as well, and one person said it would occasionally happen for no apparent reason.
I had them set their prefs to use the plain text editor by default, and that fixed the text problem of text disappearing. But then they noticed another problem that affects longer posts. When a post hits the 25th line or thereabouts, the text in the editor frame starts to "jitter" each time they type a new character. (One person said it happens much earlier, around the 12th line.) This isn't quite as big a problem as text disappearing, but it's still irritating enough that they fear people will be less interested in participating in the forums.
The people affected by these problems are all using Windows (from XP to 7) and various versions of Microsoft's built-in Japanese language front-end processor, IME. I'm afraid I can't describe the issue in too much more detail, because they all live quite far away.
We hadn't noticed the issues here, but we use OS X and ATOK, our FEP of choice, gets along fine with TinyMCE. I have noticed one small issue when trying to enter text with Kotoeri (Apple's built-in FEP), which is that every now and then the first character or two of a new unconverted line will get adopted by the editor while I'm still typing, which means that it can't be converted as a group with the rest of the line. It's a minor issue, but it's also irritating as it means the line needs to be typed over from the beginning.
We don't have anyone using an Android or Linux system, so I can't speak for them. (These systems still aren't very widespread in Japan, and finding a solution that works for Windows users is going to be a priority in any case.)
I don't know how easy it will be to get TinyMCE fixed or replaced with something else, but just now our entire staff is not thrilled with the idea of using XF for our forums. (I've had them try out the editor in IP.Board 3.2 on Invision's site, and they all report that it works without any issues; so it's pretty clearly an issue with TinyMCE and not IME.) The future's looking grim for Japanese XF.