There are several significant issues with any old bike, especially Japanese bikes from this era. They were so much more reliable and had much more bang for the buck than contemporary British iron that they attracted buyers who would normally have been put off by the maintenance requirements of the British and American offerings. This means that a whole bunch of people with mediocre to non-existent riding and mechanical skills beat them to death. At the first real problem they were parked with no thought to preservation.
Now, there are many people that never learned the necessary skills trying to resurrect the old clunkers. I get a lot of these through the shop. It is almost an art form to be able to adjust valves with mechanical tappets or to gap points and set timing. Add in the non- ability or experience to recognize proper assembly and you have a poor running bike that no one can properly repair.
Many issues relate to carburation. The lack of proper storage fosters corrosion in the carb body that you can't see. Sometimes you can re-jet to compensate, sometimes you must replace the carbs.
Cylinder walls tended to rust and pit during the same improper storage. This causes low compression and smoking.
Improper or no valve adjustment will lead to burned seats, another cause of low compression.
It can't carburate properly with low compression, so it is easy to misdiagnose running issues.
As simple as the electrical systems on these old bikes are, most people, including contemporary shop mechanics, can't seem to grasp the basics. They hack things up to conform to their thoughts, rather than taking the time to learn.
If you are going to get this kind of bike I recommend finding a crabby, snarky, old fart that has been doing this for 40 or 50 years. I'm in Olympia, Wa. but surely I must have a doppelganger near you.
The CB350, IN IT 'S DAY, was a great bike. Simple upgrades to suspension and tires netted you a good handling, fast, and reliable bike. It had a horrid high frequency vibration at sustained high speeds, so limit your freeway riding. Properly set up and maintained it will take you from coast to coast.
Even by today's standards it is pretty good. With tire and suspension upgrades it will handle on par with a GT, has a performance level near that of a 250 Ninja.
If you are seriously contemplating this bike, check compression and see if it smokes. If that is OK, then low ball them on the price and be prepared to spend $500 to $1500 with someone who knows what they are doing.