In the pharmaceutical space, do you conduct due diligence on end-users/customers (e.g., pharmacies, hospitals) that place orders with your wholesalers?  If so, how do you do so and what is the scope you use (e.g., credit checks, ownership, reputation, licenses, etc.)? 

Yes and it is necessary in many countries as depending on the license the manufacturer has (can have multiple licenses, as those working in pharma know it).
Even if it is not necessary, it is advised, especially with larger end-customers as they can have an impact on how your wholesalers are paying you in the end (obviously it also depends on your contract with them, but as in every business relationship, if they encounter problems, they will try to ease the problem on all sides to allow them to keep their own cash flow and not go bankrupt - which nobody in that relationship wants if you are playing a long-term game).
How to conduct these?
1. via the wholesaler (depending on the relationship)
2. directly via agencies, where it is a paid service (for credit check and licenses only)
3. via your own professional network for reputation

I'd say it is also a good investment as relationships change. If a wholesaler decides they don't want to work with you anymore, you are then ready to approach the end-customer immediately.
In some countries these are part of the actual security of supply on certain medications.