When Voyager is chasing Kovin's ship, in the Captain's Log entry, the star-date is mentioned as 51679.4. However, after Kovin's ship has been destroyed, in the Doctor's Log entry, the star-date is mentioned as 51658.2, a date earlier than the previous log. There is no way the Doctor's dialogue in this scene could've taken place beforehand as it directly references events which took place after the captain's log entry.
If Kovin had indeed overloaded the emitter matrix on the power cell he should have been injured as well. Yet he mentioned nothing about being hurt to Janeway, Tuvok, or the Magistrate. Which suggests that he did indeed fire the weapon at Seven intentionally. Having the weapon on Voyager they should have examined the emitter matrix, and the casing on the particle beam rifle. That would have given enough evidence to prove whether Kovin is telling the truth or lying.
After Kovin gets punched in the nose by Seven, he uses a cloth a couple times to wipe blood from his upper lip, but the blood doesn't get wiped away, and doesn't even get smeared.
When Kovin said they reported the accident immediately, Captain Janeway doesn't look at the accident report nor do they attempt to have Seven identify the other assistant in the lab where she was "held."
When Lieutenant Torres is telling Captain Janeway about the incident in Sick Bay she states she "saw Kovin hold her arm." However when the incident itself happened she ,Lieutenant Torres, is not even close. She doesn't even come in to hold Seven until Kovin is on the ground. She couldn't possibly have seen Kovin hold Sevens arm if she didn't come in until he was on the ground.