Continuity — (a) This appears to be a mild retcon, a reinterpretation of events. According to Beowulf Shaeffer, "It's a fact that his [Gregory Pelton's] great-to-the-eighth grandmother invented the transfer booth..." ("Flatlander", Neutron Star p. 140). However, according to a much more recently published account, even the ARM only suspected that the grandmother in question secretly used Puppeteer technology, sold to her by General Products (Juggler of Worlds, ch. 20, hardcover p. 107). There is no actual contradiction here, and in fact Niven may have had that in mind since Ringworld. In the first chapter of that account, Nessus subverts the transfer booth system to bring Louis Wu to him.
(b) Bey’s claim of a "great-to-the-eight grandmother" seems at first glance to be an exaggeration. The Puppeteers’ first contact with Human Space was circa 2500 (Fleet of Worlds, hardcover p. 91), and "Flatlander" is dated 2645. Even if Pelton’s matrilineal ancestors were in the habit of having children at a relatively young age, and therefore had generations averaging only 25 years apart, this would put grandmother’s date of birth 250 years before Gregory Pelton was born. And Pelton is not a young man; he says "For the last 50 years I’ve been running around in human space..." ("Flatlander", Neutron Star p. 130). If we presume Pelton is 70 in "Flatlander", this would put the grandmother’s date of birth in 2325. However, this is entirely possible! In the year 2500 she would have been 175, and per Protector, in 2341, Earth’s oldest woman died at age 210, and by 2400, boosterspice was in common use (see lifespan & aging). ↵