I seem to be having a similar issue, but only with the N905B (I also own an N905 and it is not experiencing this). I have tried multiple factory resets and manually installed different firmware versions. Only the latest 3.19.5613 firmware is causing an issue.
The UI text formatting and positioning in nickel is all wrong, and the device seems to shut off during some operations like processing content. It is also displaying what I assume is the same overlapping that YarnerT is talking about.
Strangely, if I install Kobo Start Menu, koreader and pbchess, they all seem to work normally. I have installed numerous hacks and tweaks in the past, so my first thought was that I somehow corrupted or changed files on the internal SD that don't get wiped out by a factory reset. However it seems less likely since only one firmware version is affected.
I've uploaded some pictures of the the black unaffected N905 on the left, and the problem white N905B on the right:
http://imgur.com/a/tHlyx
This device has nothing important on it and I won't be bothered much if it gets bricked, so I'd be grateful if anyone has any tips or ideas to try out.