It is in fact true that Arthur Conan Doyle was friends for some time with Harry Houdini. Although Houdini insisted that Spiritualist mediums employed trickery (and consistently exposed them as frauds), Doyle became convinced that Houdini himself possessed supernatural powers, a view expressed in Doyle's "The Edge of the Unknown." Houdini was apparently unable to convince Doyle that his feats were simply illusions, leading to a bitter public falling out between the two.
Spouses Arthur Conan Doyle and Mary Louise (Touie Doyle) are played by real-life husband and wife Stephen Mangan and Louise Delamere in the pilot episode.
In several episodes Houdini's mother calls him Ehrie (this is seen in closed captioning). Ehrie was his childhood nickname, and its similar sound to Harry influenced Erich Weisz's choice for a stage name.
In real life Harry Houdini was 5'6" tall and Sir Arthur Conan Doyle was 6'1" tall. In the TV series Stephen Mangan, who plays Arthur Conan Doyle, is 6' tall. A height is not given for Michael Weston, who plays Harry Houdini, but it is clear he is much taller than 5/6".
In this show Michael Weston portrays Harry Houdini, who works with (then-Dr.) Arthur Conan Doyle to solve murder cases in turn-of-the-20th-Century England. Michael Weston has made two guest appearances on Elementary (2012). That show portrays modern, New-York-City-based versions of the characters Sherlock Holmes and (originally John) Watson, both of whom were created by the real Sir Arthur Conan Doyle.