Is the certifier accredited?Look it up with the body, not only on the logo.
Does the scope cover this site and this activity?A for one site or product says nothing about another.
Is it current?Check the dates, and whether surveillance audits have taken place.
Which standard is it?A , and a GFSI-recognised scheme aren't the same thing.
Are audits ever unannounced?FSSC 22000, for example, requires at least one unannounced surveillance audit in each three-year cycle.
What did the audit actually find?A shows the outcome, while the report shows the findings. Ask for it.
Who else was involved?If the auditor also advised on the system, ask how independence was protected.