Jon,
All Morgan's do have some form of potential issue, with the earlier cars pre cuprinol treatment of the frame . chassis not galvanised, steel bulk heads and inner wings, have a propensity to rust and frames deteriorate often requiring rebuilding at some point. Later cars with better corrosion resistance still have potential problems eg PCB, EGR even the last GDI engines have gumming up issues , sagging rear springs, you still get rust bubbling on some of the latest trad and CX cars . Some trads have lower ground clearance than on earlier cars and so on But taking your time and working out what is the best for you, what model year and car to go for taking both potential for issues and the cost of ownership and daily running cost eg exposure to emissions charges and so on, especially if you want to tour are all things to consider,
I've had 3 4/4's and enjoyed them all, I've gone for a 2012 Plus 4 for the Duratec engine, Mazda gearbox and still galvanised chassis and must admit even though I had a more powerful Roadster, I'm finding the balance of the Plus 4 extra power over the 4/4 very enjoyable and more usable than I did in the Roadster, although ultimately the Roadsters are a flying machine limited by the chassis.
I know in the next few years, I'll be moving to a CX auto, just for the time being I'm enjoying stirring the gearbox, but if I want to continental tour again then a CX will fit my needs more and Sue can drive it more easily than a trad. Best of luck with your search.