After Chakotay was summoned by Captain Janeway his recommendations for seeking guidance from the Ankari was not taken well by the Captain because she said "...they're 50 light years in the wrong direction." It's been established that Ransom made contact with the Ankari before they made enhancements on their warp drive, they traveled 10,000 light years in less than 2 weeks. So if the Ankari were indeed 50 light years from Voyager in this particular moment then how'd the crew of the Equinox meet them before they traveled 10,000 light years? It should have been said that the Ankari were 10,050 light years away.
During the time when the Doctor got his mobile emitter from Henry Starling there were times when they (the crew of Voyager and the Doctor) had to figure out how it worked. During the scene where the Equinox EMH is being told how the Voyager EMH is able to leave the Sick Bay because of the mobile emitter he should have no idea how the emitter works and therefore not able to use it to escape to Voyager in the first place.
In the beginning, Maxwell Burke says the charging cycle for the shields takes 45 seconds. When Ransom orders the shields down and a few seconds later asked how much time. To which he got the reply 30 seconds. However the amount of time that has passed is only 7 seconds. Clearly not 15 seconds.
The Equinox was brought to the Delta Quadrant by the Caretaker before Voyager. The Caretaker was not able to send Voyager back because the Caretaker was dying and there was simply "no time" to send them back to the Alpha Quadrant. With this in mind you could say that the Caretaker should have been able to send the Equinox back to the Alpha Quadrant; however, the specifics of the Equinox's encounter with the Caretaker are unknown. They may simply have been released and/or fled rather than try to communicate and reason with the Caretaker the way the Voyager crew did.
Maxwell Burke is referred to, onscreen and in the credits, as a lieutenant commander - yet he wears the rank pips of only a lieutenant.
When Max is downloading the schematics for the field generator the shot of the ladder which leads to the lower level is seen with no one on it. Yet it cuts back to BElanna climbing the ladder in full view of the top level, when she says "Intruder alert." She could not have climbed the ladder that fast. Clearly a mistake by the editors.
As Captain Janeway is helping Captain Ransom on the Equinox bridge she says the crew calls him by his first name. The fact is that only the first officer is shown to be calling Captain Ransom by his first name which is what Chakotay does to Janeway. So her statement is irrelevant to even mention at this point.
After the speech given by Captain Janeway welcoming the Equinox crew on board Voyager the crew disperses and leaves the mess hall. When the doors close a glimpse of a ladder is visible.
Although Captain Janeway tells Commander Chakotay to bring the ship to Red Alert status, no alarm is heard.
In Relativity (1999), Admiral Patterson introduced Captain Janeway to The Doctor (EMH). The Admiral tells the Captain that it's a new system. With this in mind in combination with the supposition that the Equinox is already in the delta Quadrant, it is unlikely that this new system was installed on the Equinox.
The EMH on the Equinox in the research lab asked how the Voyager Doctor was able to leave his Sick Bay, the Equinox EMH should not be able to have left his Sick Bay either considering the EMH-2 said "The EMH-1 is designed to function in Sick Bay only." How was the Equinox EMH able to appear in their research lab when that program was only able to function in Sick Bay only?