Common-mode voltage outside the specified range
There wouldn't be an a priori way to determine what the failure mode is.  

The good news is that since you're not exceeding absolute maxima, it's fairly safe to say that the failure mode will be repeatable, but that doesn't help you know in advance what it is.

My guess is that under your use scenario, the manufacturer would be wary about timing issues.  I suspect lock up will be an issue.  Will it be within your needs??  Hard to tell, as I don't know what they are.  There may also be thermal issues, and bias current issues.  If this is important, serious testing would be in order before you run with your proposed design. Such testing is expensive with regards to time and money.

I suppose my biggest point is that you've done your job well, and identified that this part isn't for you, unless you somehow tweak your design (like with the zener I mention in comments).