I'm not sure about direct quotes from the book being scientifically accurate or not, however I can provide you with some information about the scienctific theories upon which the book is based. I have found two very interesting and scientifically sound articles from well respected scientific publications from which quote.
The first article discusses the biological references in The Time Machine. According to Mark Brake and Neil Hook in "Darwins Bulldog and the Time Machine" the novel "has two major themes: evolution and social class. Both subjects are ingeniously explored in a voyage of discovery through the invention of a machine, which is central to the book’s concern with the dialectic of evolutionary time. The machine itself symbolises the power of science and reason. The Time Traveller sets out in his machine to navigate and dominate time, only to discover the grim truth: time is lord of all. The real significance of the story’s title becomes clear; Man is trapped by the diabolical mechanism of time, and bound by an inexorable history that leads to his inevitable death and extinction signalled by the new science."
The second article discusses the science of time travel itself. "The effect, known as time dilation, occurs whenever two observers move relative to each other. In daily life we don't notice weird time warps, because the effect becomes dramatic only when the motion occurs at close to the speed of light." Check out the articels for more information.