Greetings from a new rider!

What kind of "quirks"? Do you mean the unusual design or is it doing something odd?

Welcome to the forum. Please add your location to your profile so that you don't have to remember to tell us every time and we don't have to keep asking when you forget (see Forum Settings link in my signature).

And welcome to the world of antique vehicle ownership (they own us, not the other way around). Your bike is about 4 decades old and may or may not have had all of the maintenance necessary to keep it safe & reliable so it is highly recommended to download the Factory Shop Manual for your model (available through the CX Wiki - link in my signature) and go through all of the service procedures, regardless of whether your bike has reached the specified mileage.
Note that while aftermarket shop manuals are pretty much necessary for people without factory training to work on a lot of makes & models of bike the FSMs for the CX/GL500/650 family of bikes are so well written & laid out that the FSM is really the only book you need and and the aftermarket books are secondary references at best.

I also recommend looking on all rubber parts with suspicion because rubber does not age gracefully. Check the date codes on your tires and replace them if they are over 5 years old no matter how good they look & feel (old rubber simply cannot flow around the irregularities in the asphalt well enough to grip, especially if it is cool or wet).
It looks like your bike may have the original rubber brake lines, which should have been replaced every 2 or 3 fluid changes (= 5 or 6 years) so if your bike still has them I recommend shopping for modern stainless braided ones (they last practically forever and double the life of the fluid).
And don't forget things like the rad hoses and the boot between the engine and swingarm (they can crack on the bottom where you don't see it).