Honda-SOHC

Obvious check, starter clutch sprag, it's engament and ability to turn the motor.

There was updated material specification for them  .... should be in there on later build apparently  ... no way to really check parts. It should though engage instantly, not hear it dragging without crank turning (slow moaning / screech) and fire it pretty promptly.  Not helped if battery is low or not up to scratch in giving the sprag a good "hit" to get bite and rotation.
If slow from battery, don't keep doing it as it won't help lifing.

Fork seals, check for weeping as they can get a bit gummy.

Rear brake caliper gers alot of water as underslung .... give pedal a good squeeze, then roll it back and forth to asses release.  Not hard to service, with two slide pins and lubrication of pistons etc. It will need reasonable and regular inspection if used year round, though not a show stopper.

Tires, check for alignment as wheel beeds are very well toleranced and resistant to popping the tire up onto correct place to run true. They're tubless too.

Must run antifreeze all the time, not water.

Generally tough and reliable overall.

Great torque from motor, like a diesel bus  don't need to rev much for pace. Feel very different to many fours in character, can feel a bit top heavy with full tank, though steer very neutral considering they're not race rep type bike. Easy going to ride, you've got to load the pegs and muscle the bars if you really want to get them moving fast.

Nice bike to own.

Soon I am going to look at a friend's Triumph Daytona 900 which he is selling.  Has anyone here owned one and is there anything I should look out for.  It has only done 4K miles.

Welcome to the forum Kev. I joined about a month ago and I have had lots of great advice and help already from carb rebuilding to removal of seized oil filter bolts. This is a great place to learn. A really supportive and knowledgeable bunch.

You're making the assumption that I've said it needs more power (supplied by the Boyer ? ) which is not what I've stated.

I agree it doesn't, there's other attributes within that system that hold value in this performance arena.

Question .... can you describe the failure mode within the combustion chamber which gives erratic acceleration response as you've described it ? In other words, why are you not getting a perfectly linear response with the settings you have.

Honda never state (as far as I appreciate) that you have to use equal idle circuit settings, just a suggested start point, from which their setup routine .... well written in my view ..... will allow settings for individual cylinders in giving long term combustion equality. Thats just normal in my reading of their factory instructions.  It goes further in the later PD carbs, such that it calls for correct settings, then to record those individual adjustment as the genuine reference point from then onwards.
Also it states that they are set in this way at factory, advises not to arbitrarily adjust them without making good record of their factory position BEFORE working on them.
Sensible, I feel.

Welcome to the forum Kev - enjoy¬