Short answer: no, there will probably never be format issues.
Paper wallets are in a better spot than audio tapes because they degrade less over time and there is no specialised hardware required to read them. It's not that the method of how audio was stored on audio tapes has been lost to history, it's just that finding a machine which implements that method is getting more difficult. Since the method of storage in a paper wallet is just text, it would take a pretty fantastic catastrophe to wipe that knowledge from the planet. You're right that it's important to note the specific format in which private keys have been stored. But as long as you know that, you will always be able to recover the private keys, which are the fundamental method of bitcoin ownership. Since the "import format" is just a method of recording these private keys, that makes your paper wallets as good as any digital one.
Long answer: a fundamental break in the current methods of cryptography wouldn't cause any format issues, but it might cause other issues (assuming the Bitcoin network at large had enough warning to survive the problem itself. If it happened faster than that the world would have much bigger problems than Bitcoin failure). If this happened, it would be major news and any reasonably attentive person could ensure that your paper bitcoins are at least as safe as anyone else's. Left ignored in this unlikely scenario, it might be possible for someone else to steal your bitcoins. Otherwise they could be invalidated by a protocol upgrade if the network considered that preferable to mass theft (old digital wallets would be just as vulnerable as paper ones, leaving a lot of bitcoins up for grabs by motivated adversaries).
Cryptographic protocols are often eventually weakened. But this tends to happen at least somewhat slowly (which is the main reason we use cryptography for anything important at all). A weakening of the cryptographic protocols at the heart of the Bitcoin algorithm would have far-reaching consequences for the entire computing industry: banks, governments, corporations, etc. would all be scrambling to respond. You would hear about it. As long as you followed the convention Bitcoiners eventually settled on for responding to the threat, your bitcoins would be fine. Or the world would end. One of those two.
Paper wallets are also vulnerable to burning in the event of nuclear holocaust or a large asteroid collision.
tl;dr: to be paranoia-level safe you would want to ensure that someone is at least generally keeping abreast of Bitcoin news.
