Risks to address:
People treat the reusable cups as disposable anyway. I don't see a *massive* chance of this happening given the financial incentive to not do so. But maybe have a discount program where returning used cups also reduces the cost or fills your Starbucks account.
@cassidyjames
another downside is that employees would have to handle potentially dirty cups from customers, and thus reducing the overall hygiene level of any of the drinks prepared, as well as for instance other foods such as sandwiches handled.
#Shell and several other shops with *self-service* hot beverage booths here in #Norway do allow you to bring your own cup though; if you don't bring one, you usually have to pay about 10–15 Norwegian kroner (≈1.11-1.66 USD) for a paper cup.