Here's what we do as part of a boiler service:
A visual check of the boiler and flame, if possible Checks on the flue (externally and internally)
Checking the operating pressure and / or heat input.
Checking safety devices.
Check case seals for an effective seal.
Boiler casing removed to check all main boiler components (burner, heat exchanger, main injector, spark / sensor probe).
Boiler fired safely to identify any working faults.
Boiler parts cleaned, if necessary.
A service report showing everything the engineer has done.
All relevant 26:9 checks as stated by Gas safe.
All relevant checks as stated by the manufacturers instructions.
A flue gas anaylasis check.