You betcha, and I've had it happen. In my case, the inspectors had come a long distance at the request of a local who was warring with the FBO owner. He knew we were flying out of the terminal, and he thought a good way to get at the FBO owner was to get us. The inspectors showed up, and immediately informed me that I had an illegal seatbelt installed, and that my compass card was missing.
I said golly gee whiz folks. Let's UNLOCK the airplane and check that seatbelt...and let me remove the window covers so we can look at the compass that's covered up inside that LOCKED airplane...howzabout that? We've had someone snag a data tag off one seatbelt (imagine that!)...and sure enough, our compass card had magically gone missing.
That the person who called the FAA had been the one who altered the aircraft was obvious even to the two gentlemen who stood before me with mismatched socks...but having made a five hour trip, they weren't about to have made it in vain.
In my case, I knew that a good maintenance program always keeps a record of the compass swing, and I was able to restore the compass card with just a phone call and a fax. The seatbelt I replaced, and they were happy.
You are right...an illegible compass correction card is an airworthiness item, and must be corrected. Probably a good time to go swing the compass again. If you've never done it, why not get with a mechanic and go swing it. It will be a good education for you...and when the next aircraft needs doing, go do it with a student and the mechanic, and teach the student something in the process.
This summer I saw a government inspector tag a public use aircraft for failure to have a legible compass card. I've seen it a few times over the years...generally it's when the inspector is looking for something (usually won't make a federal case out of just the card...but it can always be added on to other things found, or used if nothing else can be found)...there's no reason why a clear, legible card cant' be in place.
Mention it to the owners or operators of the aircraft...and if you're of a mind to do it, volunteer to help put it right if it will motivate them to action. It's probably something you haven't done in an airplane before, and once again, it may even prove educational.