I have a rather old Thanksgiving Cactus which is very healthy, but most of the veins are thicker or 'bulging'. Is this something to be concerned about? Actually not a new problem.

Not anything to worry about. Just like a tree trunk that grows in girth (not length) with age, the stem in the meddle of the "leaf" is anatomically the same. All dicots (that includes Thanksgiving and Christmas cactuses) have this ability. Some do it more so than others.