What Buyers Get Wrong

Buying on price per stop. The number that matters is cost per failure — a rejected specimen, a repeat draw, a delayed result, a rescheduled procedure. A carrier 15% cheaper that costs you one rejected specimen a week is not cheaper.
Assuming compliance instead of verifying it. "HIPAA trained" on a website is not a training record. Ask for the record and time how long it takes to arrive.
Not asking who actually drives. Fleet size is irrelevant to you. Ask who is assigned to your route and who backs them up, by name.
Treating tracking as optional. It's the difference between managing a delay and discovering one.
Skipping the escalation path until the night you need it.
Confusing coverage with capability. A courier who covers your city and one who runs a validated cold chain into it are not the same vendor.

Where Buyers Overpay

OverspendFix
STAT rates for predictable workVolume that recurs on a schedule belongs on a route
Waiting timeBetter stop sequencing eliminates most of it
Redundant vendorsEach carries its own minimum
After-hours premiums on non-urgent workMove it into the standard window
Re-delivery feesUsually caused by access data never collected at onboarding
Low-volume minimumsRide an existing route instead

The Single Biggest One Is the First

Organizations routinely run on-demand deliveries to the same addresses on the same days and pay dedicated-trip pricing for work that was always going to happen.