First problem I had is the same as every single cloud platform for stuff we have on desktop already (like cloud IDEs) why can't I customize things? Why can't I do simple stuff like hide my channel list/tree? I saw someone asked this feature via Twitter 2 years ago and Irccloud account replied "request accepted" or something and still nothing.
Second more serious issue is chat history. It simply doesn't transfer from one device to next. If I have it open in one machine and open it on another the last instance will lose ALL latest chat history (in my testing at lest 30 minutes worth). This to me breaks the whole concept, you have no product. Whole point of this service is to provide easy access to the same IRC instance from anywhere, but if there is no chat history/log it doesn't provide that, it would be the same if I just joined with another client which I can do for free from multitude of different web based IRC clients.
It's cool that you try to improve IRC, but first you really should probably get your product in working order.