I'd start by identifying all the components associated with it. I imagine them to be:
The
mast, the mast-step (where the
mast sits on the boat), the stays + shrouds (wires that hold up the mast), the chainplates (the places on the
boat where the stays + shrouds are hooked to).
Each component listed above has several items associated with it that you'll want to check out.
The mast: Does the mast itself look good, or are there signs of
corrosion? Are the doohickeys where the stays + shrouds connect to the mast worn in any way (elongated holes, cracks, corrosion) ? A magnifying glass helps when looking for cracks in
hardware. Don't forget to inspect the blocks + pulleys where your halyards run through - is there a lot of play in the blocks? Are the mast attachment points sound, and free of cracks / etc? Are the halyards themselves looking frayed and worn?
The mast step: Is the mast attached at the
deck of the boat ("deck stepped") or does it continue through the
deck and onto the
keel of the boat ("keel stepped")? When sailing, as the stays hold the mast upright, a significant downward force is applied by the mast to the boat. Make sure the support system inside the boat is strong, free of
rot /
corrosion / whatever. Particularly for deck stepped mast, where there will be various architectural elements inside the
cabin whose purpose is to take the downward force the mast is applying to the deck and distribute it down to the
hull and / or
keel.
The stays / shrouds: Look for "meat hooks" - wires that have broken and are sticking out. Easy to feel for, be careful not to hurt yourself. Look for corrosion, particularly at the fittings on each end, especially the bottom. Look for cracks in the fittings.
The chainplates: These babies are important, they pop up through the deck and provide the place where your stays + shrouds hook up. Look at where they are actually attached to the boat - are the bolts good, are what they are bolted to (usually some sort of knee / buttress / whatever) sound + free of
rot? Most often the chainplate metal itself corrodes where you can't see it, where it passes through the deck.
Removal +
inspection is a smart thing to do when you buy an old boat.