Suspension wise, check for worn/split ball joints, broke link bars, snapped coil springs, check the various bushes for visible damage. If you can hear clunking/knocking while driving chances are somethings worn. Its sometimes hard to feel for play in some suspension components, so a visible check is the best you can do, which is basically what the MOT centre does anyway.
Cars with torsion beam rear suspension often fail due to the rear trailing arm bearings collapsing.
Fluid leaks from power steering pumps are fairly common, if the ps pump is covered in fluid it will often fail, most people just clean them off before a test and they pass.
Corrosion in structual places near seatbelt/seat mounting points, also check for corroded brake pipes.
Brake pads condition, wipers, lights (inc beam alighment), horn, washer water, tyres, holes in exhaust system are the other things to check.