Corrected entry: While Ensign Ballard is trying to dazzle Torres, she switches between English and Kobali. Torres gives her a look and when questioned, she tells her, "You were speaking Kobali." Others in Engineering are also directing strange looks toward Ensign Ballard. The problem is that the Universal Translator should be taking care of this, causing the others to only hear what is being said in their preferred language.
Corrected entry: It is not feasible that Ensign Ballard would be able to catch up with Voyager. The stardate of her death is quoted as 51563. The episode has a stardate of 53679.4. In "Hope and Fear" (stardate 51978.2), Voyager uses slipstream technology to jump 300 light years. In "Timeless" (stardate 52143.6), they use it again to jump 10,000 light years. In "Night" (stardate 52081.2), a spatial vortex gets them 2,500 light years closer. In "Dark Frontier" (stardate 52619.2), though avoiding the Borg has added 2 years to their journey, they use a transwarp coil from the Borg sphere to shorten their journey by 15 years (roughly 15,000 light years). In "The Voyager Conspiracy" (stardate 53329), the crew uses a graviton catapult to cut 3 years off their journey. All of this happened between Ensign Ballard's death and her return to Voyager. With all of these massive jumps, the only explanation for Ensign Ballard being able to catch up with Voyager is that the Kobali have amazing technology for travelling at extremely high speeds. However, if this is the case, Janeway would have asked for the technology in return for Ballard.
Correction: Several species have been shown to be capable of traveling considerably faster than Voyager, so it's entirely possible that the Kobali can, too. Trading a person for a piece of technology would be morally questionable, at best.
When has being "morally questionable" ever stopped Janeway? Hell, she traded bio weapons to the Borg in exchange for the use of their technology to get out of their space, and she was perfectly willing to give the Equinox and crew to the aliens to appease them, to name just a couple of examples.
Corrected entry: When Lindsay Ballard explains to Janeway what happened in regard to her death (in order to prove herself valid), she said that she fell victim to a Hirogen trap 3 years ago. The problem here is that since this is the series' sixth season, three years prior would make that event occurring in the third season. However, Voyager didn't encounter the Hirogen until season four.
Correction: The entry assumes that exactly one year passes per season, however, I'm sure there is at least one episode that proves otherwise.
Correction: Given only a few words of the language had been spoken, the computer/translator would have not yet learnt the language. There have also been many times the universal translator is unable to translate some languages.