Captain Janeway gave the Hirogen holographic technology during the fourth season story "The Killing Game." In the three years since then, however, Voyager has traveled over 30,000 light years towards the Alpha Quadrant due to unique and exceptional circumstances that normally would have taken the ship decades by itself (a stolen Borg transwarp coil, slipstream technology, subspace corridors, etc). How then are the Hirogen with the holo tech found in this region of space?
At the end, the Hirogen compliments Captain Janeway saying "You and your crew would have made worthy prey." Janeway's response is "Thank you. I think." How can neither the Hirogen nor the captain remember that she and her crew WERE worthy prey. In fact, that is how the Hirogen obtained the holograms. Janeway and her crew were hunted as prey in Star Trek: Voyager: The Killing Game (1998), which ended with Janeway handing over the schematics of Voyager's holodeck technology to the Hirogen.
When The Doctor was beamed off Voyager his hands were in the under over position but when he appears on the hologram ship his hands are side by side.
B'Elanna enters a room with holograms of Klingons, Romulans, Cardassians, Bajorans and Breen, then remarks, "This looks like an Alpha Quadrant summit meeting." Klingons and Romulans, however, are from the Beta Quadrant, not the Alpha Quadrant.
"We can configure the array to emit an anti-photon pulse." Not so. There are no anti-photons. Photons are their own anti-particles.
When The Doctor asks for permission to go to the conference at the beginning of the story, he is refused because he is needed on Voyager. He is again being treated like a biological individual who cannot be replaced or duplicated. Some may think of The Doctor as simply a computer program, where there is no reason he couldn't simply be copied so one version could always remain on Voyager and one could go on away missions; however, his program is too complex and too large to be simply copied. In addition, in order to go to the conference, The Doctor would have to download into the mobile emitter. Voyager would still have to turn around, or wait, in order for him to return. That was the main reason for him being denied the conference to begin with.
There is a Jem'Hadar character among the holograms copied from Voyager's files. The Federation's first contact with the Jem'Hadar was in The Jem'Hadar (1994), just a few months before Voyager launched in Caretaker (1995). It is therefore not impossible that Voyager's files would have Jem'Hadar images.
As Tuvok sneaks up behind a Hirogen in an early scene, one of the production crew is visible on the left portion of the screen.
The Delta Flier beams The Doctor aboard without anyone first transferring his program to his mobile emitter. As the Flyer doesn't have hollow emitters, The Doctor should have "died" within transport.