A couple of cons that come to mind are: It's harder to get financing, since you're getting closer to running a business and further from a pure real estate investment. It can often require an on-site person, which adds to your fixed costs.
Because of some of these factors, self-storage typically sells at higher cap rates (lower price per $ of net income). That can be a plus if you're buying, since for the same amount of available capital you get more net income per year. If you're looking to build one, stabilize it, and sell it, then that would be a negative, since you'd get less money back for every dollar of net income you create. On the other hand, developing one should be simpler than other types of construction, as the required infrastructure is much less.
I think they can also be harder to stabilize (lease up) than residential property, as not everyone needs self storage.
Anyway, just a few thoughts,
Michael
PS I once rented a self storage unit in a converted warehouse/big box store. It had been vacant, and someone bought it and put car/RV storage in one half and self storage units in the other half. Something similar might work.