you generally need to get a feeling for the previous owner... do you think he has fixed all expensive parts or just he is clever and when the boat start to have too many small issues and may be some big one he is selling the boat
- get you own view why the owner is selling... there can be soooooo many issues that you can't find easily - e.g. the most important thing is you personal feeling - is it good deal or not... in general be prepared to spend additional about 20% of the paid price on the boat after buying but try to avoid paying more then that for improving fixing after buying..
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the most important and expensive thing to fix is OSMOSIS problems - you can find a lot materials how to identify it on the web.
I would look also in the :
engine,
depth sounder,
speed log,
autopilot,
electricity - are all switches working and doing exactly as expected,
meters - e.g. fuel gauge, water gauge,
turn on/off all sea cocks,
pressurized water is it running ,
water heater/boiler is it working on engine and on electricity ?
get hot water in the pipes it is running ?
is the fridge working ? fridge thermostat does is switch on/off ?
is the shore power battery charger working ? ( you can just measure the voltage on the batteries with charger on and off )
is the alternator ( charge from the engine working )
cold engine start - get a hotel stay one night and try to start the engine next morning in cold weather
smoke from the exhaust after the engine is warmed up - after 15 min working ( white smoke - not good - grey smoke better - no smoke super)
engine feets - how rusty are they ? how is the rubber on the engine feets ? how much the engine vibrates ( it should vibrate actually if 3 cyl diesel )
when out of the water grab the shaft and push ist- does the cutlas bearing have any movement ?
propeller - how it looks ? if folding does it overextend ? or if fixed does it have any pitting from electolises ?
take a look on the engine oil what is the color ? does it has any white color e.g. how is the headgasket ? take a look on the color of the gearbox oil ? ( dark color is not a problem but beige color like milk and oil mix is bad)
when engine is running - before getting hot, open the cooling fluid expansion tank cap and look in the liquid when push the trottle do you see large amount of bubles forming ? if yes - not a good sign ( there should be some movement in teh liquid but not large amount of bubles)
push the rudder while out of the water - does it move ? how is the rudder bearing ?
get a hose and clean well the hull and make sure that you spray water over any single window for about 5 min get inside and check is some window leaking ?
put you nose in every single cupboard under beds and open the cover of the stern compartment and take a look
is bilge pump working - put a bucket of water in the bilge and try the automatic electric one and the manual one
when engine is running taker a look on the stern gland - do you see drips ? how much ?
when engine is running and boat in the water - does is spit good amount of waters from the exhaust ?
try the heads does they properly flush ? when you put water in the sink does it go away fast or it takes minutes ( some clogging on the way)
etc. and etc.