Your mechanic has his terminology incorrect.
Unless he removed the Cradan cover to expose the pinion and crown gears, which I doubt was done on an annual inspection, he is likely referring to the final drive splines. You did not mention the mileage on your bike but it's unlikely that you need to be concerned.
To put your mind at ease, remove the rear wheel -really, it's not
THAT big of an issue- and take a look at the splines; both within the wheel hub and the portion coming through the Cardan cover.
Worn out splines will be pointy where good splines will still have the "squared off" outer edges. A little wear is normal. You may see some evidence of wear but that's most often normal usage.
Repeating the above comments, Change final drive gear oil on an annual basis and look at the gear lube for "sparkley glitter" indicating metal. Little bit is normal. Whole bunch ain't.
Now get out there and pull the rear wheel. Eyeball the splines -and check that they were properly greased with a moly-based grease- take a photo and post it up. Us'uns can tell you straight if you have or
don't have a problem.
BTW, is your "mechanic" younger than your Airhead?

EDIT: OK, I see it's an '81 model...