The Star Trek transporter appeared in the original pilot, The Cage, as a cheaper effect (ex-universe) than having the Enterprise land. - Transporter (Star Trek)
Somewhere around one hundred years spanned the distance between the first biologically safe transporters and the launch of NCC-1701. Dr. McCoy was, perhaps reasonably, afraid—there were still problems: TOS The Enemy Within.
There were a series of staged releases for Federation transporter technology. Memory Alpha has this to say:
Production of Mark V transporters was halted in 2356. By 2371, Mark VI transporters were considered outdated. Mark VII transporters were able to transport unstable biomatter, as long as the phase transition inhibitor was adjusted. (DS9: Family Business)
Presumably, there were also Mark I, II, III and IV releases, unless some were skipped à la Windows. Also, Emory Erickson, the transporter inventor, must have had a number of pre-deployment alpha and beta versions. I know of at least two, detailed in ENT: Daedalus.
Various risks have been described, including transporter psychosis (ENT: Realm of Fear), total materialization failure for a variety of reasons (Star Trek: The Motion Picture), merging of two people during transport (Voy: Tuvix), and regression during materialization to childhood (TNG: Rascals).
These risks are described as having decreased over time.
[I]n the episode "Realm of Fear", Geordi La Forge states that there have been no more than 2 or 3 transporter accidents in the preceding 10 years. Reference is also made to the advancement of transporter technology in the same episode, where Chief O'Brien states that each individual transporter pad has four redundant scanners whereby in the event a scanner fails the other three will take over, and that he has never lost anyone having been a transporter operator for over twenty years. - Transporter (Star Trek) at Wikipedia
But how much safer was the technology in the later (in-universe chronology) episodes than when first deployed? Is there evidence beyond what La Forge and O'Brien said anecdotally? There were enough late accidents to make me think that transporters must have been very dangerous in the beginning.
Not that this really proves anything, but extrapolating from Richard's detailed answer to this related but separate question, and adding in the accident from Star Trek: The Motion Picture, I count four known accidents from before TNG and seven from TNG on.
But it would be silly to think that transporter technology had become riskier over time, right?