Since then, there's also been a revolution in ski design and performance, so I would try out some demo shaped skis and then see about getting a new pair.
For all the reasons you've read, you need new equipment. Not the least of which is the fact that, as a ski instructor, we are required to inspect equipment used by students, and direct term to the rental shop when the equipment they bring is determined to be unsafe or inadequate.
Oh yeah, one other thing. My wife is just learning to ski, and she is thinking about buying some ex-rental equipment from Ski Chalet (just to use for maybe a year or two while she's learning). Would you strongly oppose buying former rentals, or is that OK as an interim measure?
Many skis also have dampening electronics in them. (The technology goes by various names.) As the skis vibrate, the vibrations are turned into electrical energy. This is then turned back into mechanical energy by a computer in order to "cancel out" the vibrations. In effect, this makes the skis chatter less, especially at higher speeds. K2 was the first with this technology, but I believe several manufacturers have it now, usually on their higher end skis.
Finally, just in terms of material engineering, skis are lighter and stronger than in the past. A lot of engineering goes into the design and construction of skis, and they use high-tech materials. Skis really have come a long way in just a few years.
Assuming the rental gear you are considering purchasing for your wife is the newer parabolic/shaped stuff, it should be very adequate for her (and you). In fact, if you're just casual skiers it could suffice for a half dozen years or more. I got a used set of newer parabolic skis with bindings last fall for $100 at a swap for my personal use (retiring a nine year old pair of old style skis). If the rental stuff you are looking at is close to that price range go for it. If it's 2 or 3 times more and you need something right away, consider buying new. Otherwise, maybe wait until next Fall for the best ski swap deals.
To be honest, your late '80s gear is probably still safe, but as others have said there is some risk as gear ages, esp if the user were any sort of envelope pusher. And yes, the new shaped skis are better for quick turning.
My K2 Merlin IV's w/Marker Select bindings were $75 and they didn't sell. You can get some good stuff CHEAP and there are Ski Patrol members there to help and advise too!
P.S. - I left about $3,000 worth of stuff and made about 100 bucks on it #*#%*%#@*@#%
BTW - the advice and help from ski patrollers should be taken with a grain of salt. Most patrollers in this area are volunteers who have jobs outside the ski industry. Other than having gone through more equipment than most, they don't necessarily have any more knowledge or insight into gear or what's best for a particular skier. For example, I know of a patroller who ardently believes that shaped skis are awful and the worst thing to happen to the ski industry. He tells everyone to avoid them and go with traditional skis. Yet you will hear the exact opposite from ski industry experts. Best bet is to talk to the shop guys who do this stuff for a living. Patrollers can help, but its just another skier's opinion.