A mate of mine suggested, making sure the mags are off and giving the prop a pull through to check each cylinders compression.
What you're accomplishing by pulling the propeller through isn't checking compressions or engine function, but removing residual oil from cylinder walls, and exposing yourself to unnecessary hazard. Otherwise, you're not accomplishing anything.
Yes there is a point, I regularly pull through my engine (90hp) before start - always before the first start of the day when all is cold and quite often otherwise.
Really? There's something about the temperature of the engine which suggests it's best to do it when cold, or there's any advantage based on cylinder temperature? As stated before, what you're doing is removing residual lubricant on cylinder walls and causing wear, and nothing more. What has horsepower to do with the price of tea in china? Neither the rated horsepower (exactly how much hp is your engine producing when it's not running?) nor the displacement is relevant.
What are the advantages? First, if you do it regularly, it is possible to detect a difference in compression between pots. This is not through a "calibrated wrist" but simply because each cylinder can be compared with the previous and following cylinders. You will not find a small difference but a significant loss of compression will be obvious, whereas in flight it may not be noticeable. Second, if you have a stuck valve - or exhaust valve leak - you will hear this through the exhaust as you pull through. You also are likely to hear air moving/hissing within, if you have (say) a broken piston ring. None of these may be detectable either during run-up or static checks, or in normal flight. You will also hear the "click" of the impulse mag(s) as the engine turns.
It's possible to detect a difference in compression between cylinders? This is the speech of the layman. Most knowledgeable mechanics understand that engine compression means very little, while most laymen place some degree of stockin it it as a symbol of engine health. Test compression five times and you'll get five different values. Test it hot and cold and you'll get different values. Have two different people test it, and you'll get...everybody say it together...different values. Yet you can do it without a calibrated compression tester, simply pulling the propeller through by hand. Most remarkable.
You can tell if you have an exhaust valve leak by pulling the propeller through by hand? Really? It's time to give up being a private pilot and go become a mechanic, because you're on the edge of a miraculous breakthrough. Sort of like the guys who touch bare wires and profess to know the voltage and amperage to the tenth value.
Further, you're telling us that you can detect by hand what can't be detected during an engine run? Truly amazing, you are. Without test equipment and nothing but magic calibrated fingers, you can detect things with the engine that can't even be detected when it's running. Wow.
You really think you're going to hear a broken piston ring? You really think this will make a change in compression, most of the time? (it won't). You may even subscribe to the myth that piston rings lined up will cause a loss of compression, but the truth is that a broken piston ring, most of the time, will do little more for you than cause excess wear. This is why we use more than one ring.
As far as listening to the impulse coupling, this tells you nothing, and is more akin to examining your handgun by looking down the barrel from the muzzle end...it makes very little sense.
Furthermore, if you prime before you pull through, you will be "sucking in" a fuel/air charge to each cylinder which makes the work of the starter (whether it be electric or Armstrong) easier, as the start becomes almost immediate, saving cranking the engine before start, which not only wears the starter and engage assembly but also can deplete the battery. Following this procedure, my engine will routinely fire on the first turn with switches ON. If it doesn't, that is usually indicative of another problem, like oiled plug(s).
Ah, priming and then moving the propeller by hand...there's a wise move if ever there was one. Putting a fuel charge in the motor and then moving the propeller...places you at even greater risk, and if you do manage to actually get fuel into the cylinder and not draining back down the intake manifold, you're simply using a solvent to wash the remaining fuel off the cylinder walls and further increase wear as you pull the propeller through by hand.
Have you thought this through, at all?
As far as what to look for during the prefligt...the "checklist" is not the be-all and end-all of inspecting your engine. You should touch, tug on, feel, move, inspect, illuminate, and test everything you possibly can during a preflight, and that includes your engine. While you've got access to the engine, either bent down on the ground looking up through the underside of the cowl, or while looking in the oil filler door or dipstick door, use a flashlight and look around. Look for exhaust stains, fluid leaks, components of the engine touching one another (such as hoses touching baffling or the induction manifold) and causing wear, wires that are frayed or bare, fuel stains, loose or disconnected spark plug leads, etc. Make sure your oil filler cap is fully in place, as well as the dipstick. When you drain your fuel sump don't simply let it go on the ground. Catch it, feel it, smell it, inspect it...make sure not only that there's no water, but that it's really the proper fuel. Check the engine mounts and mount assembly for rust, pitting, straightness, and wear. Check for oil leaks, and fuel leaks. Look for shiny areas between cylinder heads indicating a crack or a lifting cylinder head. Check the front crankshaft seal for leakage, and the oil filter adapter (if applicable) for security...it's an AD requiring inspection on every flight, for some aircraft/engines). Verify that the air filter is secure, and check the rigging of the throttle, mixture, and carburetor heat from the cockpit for full travel, no binding.
Inspect the propeller for nicks, scratches, cracks, pitting. Small imperfections in the propeller leading edge or face can lead to cracking and failure; these should be "dressed out" with a file by a qualified mechanic ("engineer"). Check for security. Check the spinner for security. Always run your hands and fingers all over the propeller to feel it. Don't simply look. Check that the distance between the spinner and the engine cowling is the same above and below. You're checking for a drooping engine mount or buckled firewall (common on this airplane from landing hard on the nosewheel). Look for evidence of dirt or grease the cowling, propeller or nosegear. If you find any, determine if it's fresh or old, and if possible, the source. Engines, like airplanes, talk to you with a quiet voice, often warning you with little things of bigger things to come. Get to know the little things and address them before they become the big things.
Check the cowl itself for uniformity, security, and that all fasteners are in place, not loose, and without cracks surrounding the fastener holes or access. Look down the cowl from the front, across the clinders and try to spot tennis shoes, bird nests, or the odd grenade (things that ought not be there)...mechanic's tools, etc. Always be on the lookout for the things you don't find...continuously ask yourself "what is it that I've missed?" and then go find it.
Look on other parts of the airplane for clues as to the engine health. Look at the exhaust stack. Give it a tug, see that it doesn't move. Look at the color of the deposits in the exhaust; this tells you a lot not only about the health of the engine, but also it's care and how it's been operated. Look down the belly to see how much oil is there, and on the windshield to see about oil or other evidence of leakage.
Verify the starter drive (bendix drive) isn't engaged. Look for an alternator belt. Tug on it. Try to hand turn the spark plug lead connectors nearest the cowl entrance; ensure they're tight.
You needn't simply pull out the checklist and follow along blindly. Look at everything; it's all worthy of your attention. Extra time spent scrutinizing the airplane is for your own safety, and for your benefit. Take full advantage.