Here, Lewis Zimmerman is depicted as a recluse who says in his last will and testament that he "created most of [his] friends" (i.e. his only friends being the holograms he programmed). In his sole previous appearance on Deep Space Nine, he was shown to be quite sociable, even nearly getting Lita to run away with him.
When Troi walks in and sees the two doctors, she asks which one is Dr. Zimmerman. She is an empath and would usually sense emotions from the live doctor and nothing from the EMH. She even says this later on when she detects that the doctor's assistant is a hologram. However, since Dr. Zimmerman and The Doctor were in close proximity to each other, Troi may have not been able to detect which one was the human.
This takes place in 2377, and Doctor Zimmerman's hair is fully gray, yet his hair was fully brown in Doctor Bashir, I Presume (1997), which takes place in 2373, only four years earlier. However, it's not unusual for someone's hair to go gray in that amount of time.
Dr. Zimmerman orders the computer to deactivate the EMH, but as has been established, the EMH from Voyager has the ability to ignore that command. However, that ability may have been limited to within Voyager.
In shots in which Dr. Zimmerman and The Doctor appear together, they rarely match one another's eye line.
In shots focusing on Zimmerman where the Doctor is viewed from behind, the body double used for the Doctor is conspicuous in having darker hair and broader shoulders than Robert Picardo.
When Zimmerman disables the Doctor's mobility subroutines and he declares that he cannot move, he can be seen visibly wobbling in place.
The Doctor claims to have come up with a potential cure for Dr Zimmerman's terminal illness but only he would have the knowledge and skill to do it. The Doctor is a computer program. Voyager could easily transmit the Doctor's cure to Starfleet and have it performed by another EMH if necessary. It is contrived nonsense that the Doctor *has* to go on the potentially perilous journey to the Alpha Quadrant himself.
Dr Zimmerman says to the EMH, "I didn't program you for sarcasm." In Relativity (1999), Captain Janeway is being given a tour of Voyager by a Starfleet Admiral before it leaves Earth. At one point the brand new, freshly programmed EMH is activated and makes a sarcastic comment when he finds there is no medical emergency; he's just being "shown off" to the Captain.
At the Jupiter Station, Dr Zimmerman says, "I recommend a tour of Jupiter's 3rd moon. I hear the lava flows are lovely this time of year." Jupiter's 3rd moon (among the Galilean moons) is Ganymede, a volcanically dead body. He is referring to Jupiter's 1st moon, Io, which is the most volcanically active body in the solar system. (Among all the currently known moons, the 3rd moon is actually Amalthea; Io is 5th and Ganymede is 7th.)
Counselor Troi says that the Enterprise is on a mission 7 light years from Jupiter station, as though that is a great distance. At high warp, a starship like the Enterprise can traverse 7 light years in a matter of hours.
Doctor Zimmerman attempts to add numerous subroutines to the Doctor's program to "improve" him before he is sent back to Voyager. The Doctor had to have a good number of subroutines removed in order for his file to be small enough that it could be transmitted to Jupiter station via the subspace compression beam. If Zimmerman had gone ahead with his planned additions, the Doctor's program would have become too large to transmit back to Voyager.