Well, to continue on.....
First time, that is after several months of frustration, I experienced the reading difficulties, I got a disc cleaner and cleaned the laser according to instructions. It worked. Well, it worked for about 30 minutes that is. Thereafter, repeated cleaning never did any good. I ended up taking the player to Marantz Service Center, and problem was fixed.
Thus, it's all rather simple. If the laser has some lint, dust, etc. causing the reading problems, then cleaning the laser should cure the problem. As stated above, this is the usual first step, as it's easy to do.
But if the problem is caused by the overheating chip, then cleaning the laser will do nothing for that. The overheating chip is a well known issue with the 8260 player. Marantz eventually acknowledged the problem and issued a service bulletin to the Service Centers. I always thought that since the problem was the Marantz design that they should have fixed the problem for free, but no luck on that.
At least the problem is not fatal like in the Philips SACD 1000.