Charge state first, because that is what fails shipments, and it is the one thing you cannot tell by looking.
Verify the Charge, Do Not Assume It
Weigh the unit on arrival and again after any top up. Weight is the only practical measure of how much cold mass is genuinely in the matrix, and an undercharged shipper is the commonest cause of a failed cryogenic transport. Confirm it has been inverted and drained so no free liquid remains, because free liquid changes both the regulatory position and the behaviour of the vessel.
Inspect the Outside
Look for frost or condensation on the outer shell and for any cold spot on a surface that should be at room temperature. Either indicates a vacuum no longer doing its job, and a hired vessel has a handling history you did not witness.
Confirm the Paperwork
The air waybill needs the words not restricted and the special provision number A152 under the IATA Dangerous Goods Regulations. Where samples are UN 3373 Category B, Packing Instruction 650 applies to them separately. Confirm carrier requirements before booking. See the CryoStork range for owned alternatives.