I say that as an American. Sure having some Americam actors must've seemed essential to help market this British based show internationally. They did succeed at this but the writing was affected. Americans were pushed into the story. Either it was an American actor or sometimes a British actor playing an American. In one, it's an out of work actor who goes overseas to be a success, another he's a private investigator searching for his brother. In another its someone hiding from the mob. All plausible but it didn't work for me.
That's not to be very critical of the show because I still enjoy it alot. Some shows are weaker than others but the better ones are excellent and very memorable and were more Hitchcockian than Hitchcock by the middle 70s. The better episodes are more suspenseful than Topaz, Family Plot, Torn Curtain or Marnie and rival Frenzy.
Personal favorite doesn't star an American actor. Stars Patrick MaGee, Don Henderson, Joanna Pettet only plays an American. It's called A Killer In Every Corner.
The show was successful and carries on Brian Clemens' string of successes which he would continue with The Professionals (after The New Avengers hiccup). Laurie Johnson provides the score and some of this same music turns up later in New Avengers and earlier episodes of The Professionals.
If you don't mind your tv shows looking stagey and are much more interested in story and acting, then you'll love this one.