I was in the same position some years back. Was looking at C30 Tall Rig. Most of the survey was small items except the under the cabin floor mast support. Catalina built up between the keel and the cabin sole with pieces of wood that rot over time allowing the mast support, cabin sole, cabin ceiling (deck) to sink.
With the surveyor, I was able to punch a screwdriver through the forward wall of the bilge. Only way to know for sure if the wood is rotten causing the mast support post and the deck to drop. In some cases, people have been able to notice the drop by observing the margins on the head door. In some cases there are fiberglass cracks at the mast step on deck. I think there were also some vessels that had issues with wood support under the mast step on the deck -noticeable depression and gel coat cracks.
Look for signs of water intrusion - the interior bulkheads on this boat carry the rigging load to the chain plates. So the bulkheads cannot be wet or showing rot or decay.
Look for cracks around the shaft strut. Mine was not properly bedded or sealed. The cracks showed up on a sea trial for a potential buyer. This was a source of in-leakage that was evident through the floor port at the bottom of the companionway ladder.
The hatches are notorious leakers. The joke was that the fiberglass holes were factory cut with chainsaws. These can be fixed.
Look for rudder issues - bulges, fiberglass cracks, rust, delamination. My rudder leaked and I had to put in a drain to make sure any interior water did not freeze and do internal damage. Sea water intrusion is a long term into the rudder is a long term corrosion issue. If you remove the emergency rudder cap and use a bright light, you can view down the rudder post for water. I ended up removing my rudder and rebuilding the forward, aft and lower edges and cut out two delaminated areas to cure the issue at home over the winter. If you are into it, there are a few rudder rebuild videos on youtube.
Keel bolts should be in good condition - leaking from below is a bad sign - but this may be difficult to determaine solely from interior. I belive the Catalina smile issue was fixed by this year so that should not be an issue - Catalina used wood in the keel stub. Over time the wood rotted and the keels tended to drop creating the "smile".
Also have your surveyor evaluate the deck moisture - I believe (but not positive) that this deck was balsa cored.
Look at transmission oil - normally bright red ATF. If dirty or brown you may have a rebuild/replace in your future
My engine was a Universal - there are several sizes. It would be helpful if you could do an engine compression check- Harbor freight has a diesel compression check kit.
On an older boat, standing rigging is always a concern. You and your surveyor should look for rigging issues - clean swages with no cracks or broken wires, etc.
If you buy - and it was a great boat
1. Verify you don't have the original plastic throttle and shift levers at the helm - change if req'd
2. Verify the throttle and shift levers operate easily
3. Remove the heat exchanger end cap (zinc end) and check the cleanliness of the tubes and remove any broken zincs - the tubes can be boiled out using muriatic acid dip or take it to a radiator shop.
4. If you have a diesel (universal) - these were several different Kubota tractor blocks. You can get most parts at your local Kubota dealer if you go in with the part number - There are complete engine manuals available on the Catalina 34 website and other places.
5. A lot of the teak can be removed and finished at home during the winter - I was able to remove, finish and re-install my cabin-top teak hand rails by unscrewing from below and did not have to remove the teak surface plugs.
6.There are a lot of places for water to leak in, I re-bedded all deck fittings and fasteners with butyl tape - see Maine Sail
Marine How To - DIY for Boaters - Marine How To
7. The outhaul may need upgrade and attention. There are some on-line directions on how to add to the outhaul pulley ratio. The removal of the boom end cap screws will be a challenge - The Harbor Freight Impact Screwdriver was invaluable in this effort - don't even try a normal screwdriver past normal screw removal force - once you strip the Philips head your into a lot more work.
8. If the mast is down, consider adding an elbow to the conduit coming from the cabin roof. This will reduce water down through the mast and conduit.
9. We bought a 2" queen mattress topper for the v-berth. Lay it out on the cushions at home in the fall. Cut, glue and sew. We wanted one that came with a cover to minimize the dirt that foam attracts.
10. Check condition of cockpit drain hoses (and other seawater hoses) - replace if req'd.
11. This should probably be at the top of the list - remove the factory "gummy" plugs in the electrical harness. One in the engine compartment and one behind the cockpit wiring panel
12. You can improve the icebox performance my wrapping with rigid foam and sealing with Great Stuff
Good luck. Let us know how you did