There are two issues I’ve read about on the forums here (primarily bug report). The first I can personally confirm is currently happening, but is not terribly serious. The second I have not personally tested, but is related and far more concerning.
The first is if you place a unique or unique(number) item in the warband bank, it will not be visible in the warband bank from a character with the same (or too many in the number case) unique item. If you search the forums by terms such as unique items warband bank, you’ll see some of the recent threads describing this. The resolution is to access the warband bank from a character that does not have any (or too much) of that unique item.
The second, far more worrysome one involves placing unique items in the warband bank leading to the deletion of said unique items. Memory of Kalimdor disappears from Warband Bank? - #2 by Khorbyn-moon-guard and Items are dissapearing after being put in the warband bank - #8 by Cysgodi-dalaran describe it in two scenarios.
Thusly, please, please be very careful when depositing unique, or unique(number) items in the warband bank for the time being, or just avoid it entirely.