I just went through this process on for my much smaller Contessa 26; The Contessa is a very simple boat and I still felt it was necessary to get out and test the systems.
Having said that, here's what I learned...
1. Find someone skilled to do the sea trial with you.
I hired someone who turned out to not live up to their resume. This has resulted in a few unexpected surprises that I found on my 6-week shakedown cruise.
2. Test all systems, not just 'go for a daysail'.
Some things my sea trial didn't turn up (because we only tested the sailing system); The head pump wouldn't "un"prime itself, New pump; The galley faucet leaked, replaced 3 O-rings; The galley pump dribbled, siliconed the pump seal; Ice box drain was plugged, unclogged with my universal coat-hanger tool.
3. Don't "be lazy". Put up all the sails. Try all the halyards. Try different track settings.
The guy I hired barely looked at the genoa, I found out last week that the UV protection was rotted and now it's removed and replaced with a foresail cover - $500. Secondary mainsail was covered in mildew (which I expected but never verified) and was later sold. The topping lift is incorrectly rigged under the radar bracket. The genoa cars and traveller had not been changed position in 5 years so they were slightly seized, a little lubricant eased them. Boomvang had seized over the winter.
--- the only thing my lazy sea trial surveyor commented on was the boomvang... which I had pointed out.
4. Check the engine.
An engine might run quite happily for 30 minutes, until warm. An engine might start up easily, if the previous owner has always warmed it up before you got there. Make sure you give the engine a thorough workout... it's the single most expensive piece of equipment in an older boat.
For other boats, I'm sure you have other systems and so-on to check. Water, sewage, air conditioning, manual/auto bilge pumps, dinghy/motor, windvane, autohelm, radios, radar etc.
Sometimes you just need to get your hands dirty and have someone with you. Even if you're new to sailing or boating, you can tell if something isn't working well.
Best of luck,