I am reluctant to copy from the BA company forum, but I think on balance it helps clear up some of what is being discussed, and shows what a "major" carried out prior to the ban being lifted. The post relates directly to the test flight BA carried out in a 744.
All the filters in the aircraft were replaced before the flight. After the flight, they were all removed and sent for analysis - the theory being that any contamination of the filters could only have occurred on that flight. Nothing was found. Fuel and oil samples were also taken and they came back clean too. The engines were boroscoped and showed no evidence of any damage or accumulations of ash deposits. The airframe (including windows) was examined for any signs of abrasion - none was found. The QAR and FDR data was sent for analysis to detremine is there was any abrormal relationship between engine parameters (eg erroneous EGT for the N1) or air data parameters (eg Angle of Attack incompatible with IAS) - again nothing has been found.
The aircraft was deliberately flown in areas where the Met Office Model showed that ash encounters were likely, but outside the areas where the WSI model showed ash encounters were likely (you might like imagine these areas as being similar in principle to the Enhanced Procedures Zone and the No-Fly Zone respectively, which the CAA has mandated in FODCOM 12/2010 )