So when the Third Incarnation of the Doctor accidentally phased himself into the "Evil Mirror" TV dimension, as seen in "Inferno", what happened to the evil Doctor who should have been there?
As I stated earlier, the Universe probably can only handle one Time Lord known as the Doctor in a particular dimension at a time. So when the Doctor of Earth Prime-Time crossed over, the evil Doctor must have been shunted over to the main Toobworld to keep a universal balance.
The only problem was... when the Doctor of Earth Prime-Time returned, the evil Doctor stayed put there as well. He probably had no choice - if he was also stuck with a stripped down console from the TARDIS, it could have malfunctioned and left him without any method to get back home. (He may not have had an Earth to go back to by the looks of how "Inferno" ended, but since the Evil Mirror dimension has appeared in later shows like 'Star Trek: Deep Space Nine' and 'Buffy The Vampire Slayer' and even 'Community' - its appearance on 'Hercules: The Legendary Journeys took place long before on the Toobworld timeline - then for Toobworld Central purposes I'm going to say that world survived. Only that particular area was destroyed by the cracks in the earth's crust.)
When the Doctor arrived in that evil TV dimension, he found himself basically in the same situation as the one he left (drilling through the earth's crust to obtain Stahlman's gas) albeit in an England which was a fascist republic. So the evil Doctor was probably also fixing the console of the TARDIS when he was phased through the vortex. (Since it is a living entity, could that TARDIS be evil - "EEEEEVILLLLL!" - as well?)
But he wasn't at the "Inferno" site, or else evil Liz Shaw and the Brigadier and Sgt. Benton would have seen him and interacted with him. Had he been there, the evil Brigadier and his Section Leader would have recognized the Doctor of Toobworld as their own.
Just a quick note to keep things straight - the Doctor of Earth Prime-Time will be referred to as Doctor-M (for "main"), while the other Doctor will be Doctor-E (for "eeeeeevillllll!")
Wherever he landed on Toobworld, Doctor-E never made it back to his own dimension - at least that's my way of thinking. Maybe his TARDIS console was destroyed in the crossover, or when he attempted the return voyage. And maybe it was because of its damage that Doctor-E was forced into regeneration, bringing a second version of the Fourth Incarnation of the Doctor to the main Toobworld.
This Doctor-E must have accepted his fate to be stranded on a world he never knew and decided to do the best he could to adapt... and since he was eeeeeevillll!, maybe he planned to profit from his brave new world.
How? By starting a new identity as a detective for Interpol.
Even though a detective from Interpol should be on the side of law & order (cha-chun!), Doctor-E sought a position with them because it would have been the logical thing to do. (Remember, the Doctor did visit the planet Vulcan - or at least one of its moons - and must have learned from the natives about the discipline of logic and the practice of the mind-meld, which he later used on Madame de Pompadour and Donna Noble. The visit to Vulcan must have been the same for Doctor-E as well.)
A position within a world renowned police and security bureau would give him access to information that could prove useful for getting him off that backwater planet and - if not back to his home dimension, then at least back to the Gallifrey of the main TV Universe. (And who knows what kind of hell he would have unleashed there?)
I don't know why he took the name "Anatole Blaylock" as his alias while in Interpol. I checked the TARDIS wiki but neither name came up during a search of their database. It could be that it was a name that supplied by his psychic paper and nothing more.
During that next decade, Doctor-M (who by that point had gone through two more regenerations, the last one just two months before we met Doctor-E as Agent Anatole Blaylock. Doctor-M and Doctor-E never crossed paths - at least as seen on TV.
In that time "Anatole Blaylock" became obsessed with an international jewel thief known as "Le Renard" - "The Fox". Doctor-E was maniacally fixated on Le Renard as Ahab was on Moby Dick. (It probably stemmed from Doctor-E's belief - shared by many incarnations of Doctor-M - that humans were but children to a Time Lord. In other words - not as smart. And yet Le Renard kept besting Doctor-E, or rather Inspector Blaylock.
We saw the story of "Anatole Blaylock" come to its conclusion in the 'Remington Steele' episode "Hounded Steele. The last we knew of him, he was in a padded cell, just saying "Le Renard, Le Renard" over and over again.
So is he there still?
I think he escaped, at least from incarceration.
He may have gone loopy, but he was still a Time Lord. Like Marvin the paranoid android (whom Doctor-E may have met in his home dimenson; it's almost certain Doctor-M had to at some point since he knew Arthur Dent), the Doctor had a brain the size of a planet.
But to escape, he'd have to "die" and regenerate.
With a new body and new personality, Doctor-E could have easily conned the orderlies into believing he was a visiting doctor (named John Smith?) who had his clothes stolen by Blaylock, and that he was locked into the cell by Blaylock. Why shouldn't he be believed? He looked totally different from the madman who previously occupied that cell and the only clothes to be found would be the prison uniform left behind by Blaylock.
While the prison/asylum went into lockdown as they searched for Blaylock, Doctor-E would have been given a change of clothes and escorted off the premises for his own safety.
As for where he is now, I'd like to think that his re-capture and forced return to his home dimension was engineered by the Eighth Incarnation of the Doctor during one of the many adventures he must have had off-screen....