A few folks are getting a tad confused when it comes to old aircraft. The problem is not being old, per se, but what that old aircraft has had done to it during the time that it got to be old.
On the structural side of things, there's lots of fancy detailed engineering stuff which goes into the stressing design of the aircraft which we can sideline for pilot talk.
The main concern is the size of the tin bits which are holding the aircraft together - in particular, the thickness of the important bits. As part of the certification, the OEM will do a bunch of sums which are proved correct during structural testing. The link to the thread on Bob Tait's website to which I referred earlier in turn links to a Boeing structural test which is well worth a watch to get an idea of the sort of stuff which the OEM does as part of the certification workup for an aircraft Type.
The end result for the initial certification is that the aircraft is shown to be OK. The problem now becomes one of ensuring that it continues to be OK as time goes by (the buzzword term is "continuing airworthiness"). So, what might be the main concerns ?
The problem is that most of the important tin bits are subject to damage associated with what we call structural fatigue. The basic problem is that the materials are somewhat microscopically imperfect when they are made during the various metallurgical processes involved in making the end products which the OEM uses to build the various aircraft structural components. As the structure is subjected to in-service operational loads, these microscopic imperfections can move around in the parent material and, eventually, enough join up to create micro voids (tiny cracks) which then get bigger with continuing operational use. As they get bigger, the structural item concerned becomes structurally weaker. Unless we can detect these problems and fix them before they get to critical states, we run the risk of bits of aircraft breaking in flight and taking everyone quite by surprise.
Related problems, such as corrosion (think "rust"), serve to accelerate (sometimes quite rapidly) the development of fatigue problems. Corrosion is a bit of a mongrel problem both at the design stage and then during ongoing maintenance. Some designs are better than others but, at the end of the day, it becomes an ongoing matter for the diligence of the maintainer folk to whom we all owe our continuing existence as being both alive and pilots ....
We have techniques, developed over the years, which are used in the certification and continuing airworthiness world to address these structural concerns. But, and that is a big but, it all depends on everyone doing their bit to contribute to the overall gameplan.
An underlying and critically important presumption is that the aircraft is operated and maintained in a manner consistent with the OEM's design assumptions. If that is not the case, then we can get to a stage where all bets are off and the OEM's assumptions and maintenance requirements no longer fit the problem. It is a matter of great regret that sometimes real world reality doesn't match the OEM's presumptions regarding its perception of what the real world should be like. In such situations, we can find structural fatigue degradation reality rapidly outpacing the OEM's presumptions which are built into the maintenance programs. The end result, occasionally, can be inflight catastrophic structural failures and an aircraft hull loss.
Such failures can be associated with, say, thunderstorm penetration ranging down to simple flight downwind in the circuit on a nice sort of day. Glen Donovan's Nomad loss, 30-odd years ago, now, was an example of the latter and is why I always utter silent profanities when I see or hear of folks operating GA normal category aircraft in an inappropriately cavalier manner.
The reality is that we do have unexpected inflight structural failures and that, sometimes, these are contributed to by inappropriate operation of the aircraft over its lifetime.