How does anyone competence check a health and safety professional or anyone for that matter?

You don't have to know everything they know but you do have to know what is required i.e. training certificates can prove they are trained, professional membership and CPD can prove they keep up to date, PI Insurance certificate can prove they are insured, sample RAMS may prove they know what they are doing and do what they say.

The list can be endless but having written records of you examining original documents of the above will go a long way to prove you are competent in assessing sub-contractor competence.

Another way is if the contractor is approved by one of the CHAS/Safecontractor type organisations. Check the approval certificates as they will have already jumped through a few hoops.

"a failure of some LOLER examiners to return and TE equipment".
They're only obliged to return if they are contracted to do so?
You don't always necessarily have to know first hand what is required, but you do have to know someone who does!
In this instance, your Insurers can usually advise. In other specialist areas, competent sources of advice can include H&S Advisers or CDM-C in a construction context.
In a wider and more pragmatic context though, are they recognised and do they do good work for others?
PQQ, qualifications and accreditations are all well and good, but ask for references, and check those references out.
It is common condition of Contract that appointment is conditional on satisfactory references being received.
As for who is held responsible when something goes wrong, well that will depend on the circumstance. Demonstrating you made reasonable enquiries regarding competency will go a long way towards avoiding a caning though!

Chris' post above is strictly speaking only applicable in a construction (CDM Regs.) context.
However I would hope these sound & pragmatic principles would apply universally in any legal proceedings.