It would be useless, and possibly harmful, to start treating for a problem until you know what the problem is. Apples are prone to many problems - insects, diseases, and cultural - and the remedies vary widely. Some are chemical, some not.
So the first step is diagnosing the problem. If you can send pictures of the damaged apples, please do. If there are problems on the leaves, those could also be important. There may be more than one problem going on, so the more information you can provide, the better chance we have of diagnosing it.
Some other information that could be relevant: Do you irrigate the tree in the summer? Does it look healthy other than the apples, i.d., are the leaves healthy green and not overly damaged? Is it properly pruned? Do the apples grow in tight clumps touching each other, or are they well separated? (Many apples trees need thinning for proper spacing). Are there other apple trees growing nearby, and if so, do any of them have the same sort of problem?

Looks like I'll need to wait until Spring to check the leaves, eh?  Below are your questions with my answers embedded.

Hi, Thomas,
Yes, at this point you'll need to wait until next season to really be able to diagnose the problem.
As for the irregular bearing, apples tend to be alternate or biennial bearers. They do as you describe, bear a lot of apples one year, then few the next. Some varieties are more prone to this behavior than others, but pruning is the primary way to control it. This publication from Idahosays "If not thinned yearly, most apple cultivars will develop an alternate bearing habit, producing a heavy crop one year, then almost no crop the next. Biennial bearing can be reduced if a substantial number of blossoms and small fruit are removed from the spurs on the tree during bloom, or within two to three weeks after petal fall. This allows many of the spurs on the tree to rest, which results in flower bud initiation for the next year’s crop. On the remaining spurs, the grower wants to set the "king bloom" and remove several lateral blooms with chemical thinners. Hand thinning is then done to remove additional fruit to achieve the desired crop load. This leaves only the stronger fruit behind which produces the highest quality and most highly colored fruit at harvest." and "Thinning the fruit by hand six to eight weeks after bloom is a very common practice. Because it is usually done after most flower bud initiation has occurred, it does little to ensure return bloom. Hand thinning serves to ensure highest fruit quality by spacing the fruit on the limb, reducing fruit clusters to singles and removing fruit that is likely to rub on the limbs. Hand thinning also eliminates fruit that appears damaged by early season insects or diseases."
So you should consider thinning your fruit the next heavy year.
See you next year to diagnose the damage issue!

Thanks for the info.  Weren't you a real estate broker?

Yes I was for awhile. You too as I recall!



Sounds like I need to prune it this spring, which has never been done correctly.  

Depending on how overgrown it is, you may need to take several years to renovate it. You'll find the info you need to do it correctly in these OSU Extension publications.
Pruning to Restore an Old, Neglected Apple Tree

Training and Pruning Your Home Orchard

You might want to try to identify the variety, as this can have an effect on how prone it is to alternate year bearing. Here are some resources.
https://www.orangepippin.com/varieties/apples
https://en.wikipedia.org/wiki/List_of_apple_cultivars