Here is a list that I've compiled so far for E/J4500s. Apply as needed to what you are looking at.
1) What brakes does it have? DLisa and EX225 are good. Other brake types: ask your local coach service company about parts and local knowledge working on them.
2) Does it use gold bricks or multiplex system? Gold bricks are hard to find and expensive.
3) If it is a DPF equipped bus, get the service history on the DPF and SCR. Has it been washed? Replaced? Deleted? Then pull the codes on the engine to read how plugged the DPF is and when it was last regened. If you can, force a manual regen and read the plugged percentage after.
4) Check engine oil pressure at idle when hot.
5) Drain a small amount of oil out of the crankcase when the engine is cold and has been sitting. Check for antifreeze. Send some away for sampling. This is especially important on the Cat C13, which is know to leak anti freeze into the oil which causes crank issues if not caught.
6) Watch engine blow by when at idle and at max RPM when cold and hot.
7) Inspect tires. Note the tread depth, condition, size and date codes. Make sure the bus has the right size tires (11s and 12s versus 315s) and make sure they are all the same. Verify which ones are recaps and which ones are virgin. Note any abnormal tread wear, especially on the steering tires as that often indicates steering or suspension issues.

Note when the bus last passed a commercial vehicle inspection. See if the inspector's notes are available. Search the bus's DOT number if it is available.
9) Inspect under the radiators and hoses for coolant leaks. Squeeze the radiator hoses when cold to see how pliable they are.
10) Inspect the shock absorbers for leaks, rust, etc.
11) Inspect hubs for leaks.
12) Check that all lights on the bus work.
13) Time how long it takes for the bus to build air pressure. Shut off the engine. How fast does it lose air pressure ? Walk around the bus and listen for air leaks. Best not to do this near a freeway where it is noisy.
14) Check all the windows in the bus. If it has dual pane windows, check for condensation. Replacement windows are expensive.
15) Check the baggage compartment and underneath for rust. Most E/Js will be entirely rust free in this area.
16) Jack up the front axle. Get a bar and pry the bottom of each steer wheel up and down. Note any play. If there is play, it is probably the kingpins, which will probably need to be replaced. Pry the wheel side to side. This is steering gear play. It will need to be fixed to pass inspection.
17) With the engine running and the bus stationary, turn the steering wheel to get a feel for free play in the steering system. I think 1.75" is allowed. Not sure. The less the better.
17) Check the disk brake wear indicators on each wheel.
18) Check the condition of the air bags. Look for leaks and dry rot.
19) Check that both alternator lights go out when the engine is running. Check the battery voltage at idle to make sure charging is happening.
20) Inspect the batteries. Note the date codes. Wouldn't hurt to do a hydrometer and/or load test.
21) Check the ABS light goes out. If not, pull the codes using the dash board. The bus probably won't pass inspection with an active ABS error light. Any errors will need to be fixed.
22) Inspect the front and rear bogies. MCI calls bogies the steel that the front and rear axle are mounted to. Bogies are made from mild steel, not SS like the baggage compartment area. Look for excessive rust, cracks and repairs. Visually check all the suspension bushings.
23) Check that the coolant heater fires up.
24) Check that the bus has a spare tire in the spare tire holder, date code, air pressure.
25) Check the brakes and steering on a test drive. Watch for smoke when accelerating. Watch engine coolant temp.
26) Inspect all the engine accessory drive belts.
27) Inspect the fan clutch for play. Look for oil leaks on the fan angle drive gear box.
28) If it is an E with a steerable tag axle, check that the tag axle steers properly when the front wheels are turned. Bus probably has to be rolling a bit to allow this to happen.
29) Remove the air cleaner. Reach through the filter canister to the air intake hose going to the engine. Is there any dust ?
30) Observe any new paint on the engine to get clues for what parts have been replaced. Idlers, turbocharger, water pump, head ? Look at the engine cradle bolts. If they are new or super clean, the engine/transmission assembly has probably been out recently.
31) Check the engine and transmission serial number against what MCI has on file. Unmatching serial numbers mean they have been replaced.
32) Check if the OTR A/C system works.
33) Thoroughly inspect the bus wiring for hacks. You want it to be all stock and working. Nothing worse than fixing someone else's hacks.
34) Pull ECM fault codes. Verify that the ECM mileage matches the odometer mileage.
35) Get any and all services records that are available for the bus. If it is being sold at a used bus yard, find out who last ran it and call them to ask about the bus.
36) Check that the tag axle lifts properly.
37) Crawl under the bus (while safely blocked up) and check for oil leaking out of the flywheel bellhousing. Oil leaking here is probably due to a bad rear main seal on the engine.
38) Inspect the drive shaft for play and any obvious issues.
I left out testing the transmission. This is an evolving list as I learn more about these buses. The MCI maintenance manual is really good at explaining things. It's available free online.
Good luck.