So - it takes 3 hours for the novolog given to peak to it's full effectiveness, whether given from the omnipod or the pen. The pen can give the correction all at once, where the pod will give it in increments, every few seconds, until the full correction is given. ( I don't remember the exact amount of time) It won't take 3 hours for the correction bolus to be delivered, just absorbed.
Many people will inject in order to get the correction immediately, not spread out for a couple of minutes.
Insulin is said to have a shelf life, once opened of 30 days - whether in or out of the fridge.
I use a vial of insulin a month to fill the pod. I keep that vial with an extra syringe in my PDM case, ready to use for such instances. At the end of the month, I switch to a new vial. I have gone over the 30 days and rarely notice a difference, but I do know people that can tell right away that the insulin is not as effective.
If you want to keep using the pen for corrections (those nano size pen caps are great!) when you get to the last week of the month you could actually withdraw the insulin out of the pen and put it in the new pod so as not to waste it.