The number of insignia pips on Ezri Dax's collar change between one and two prior to Captain Sisko informing her that Starfleet Medical gave her the rank of full Lieutenant.
After Garak berates her, Ezri goes to the Bajoran shrine on the promenade. The exterior shot shows her entering quickly, taking long strides, but when it cuts to the interior shot, she is moving much slower and taking short strides.
When sitting on the simulated cliff with Ezri, Garak says that he's aware there's a holosuite wall not 10 meters in front of him. The holosuites on DS9 are nowhere near 10 meters in length.
When Garak collapses in his shop Ezri sends a message over her com, "Dax to infirmary, I need a medical team". She never said where they were needed. Starfleet combadges are tracked by the computer. The medical team would know where to go based on her location.
The mug of bloodwine that Ezri is given and then hands back to Quark is clearly empty.
Sisko tells Ezri that Starfleet Medical has agreed to waive her final months of training and give her an immediate promotion to the rank of lieutenant. However, once she is promoted, she is seen wearing lieutenant junior grade pips (one gold pip and one black one) rather than full lieutenant pips (two gold), which she would continue wearing for the rest of the series. Further confusing matters, beginning with "Take Me Out to the Holosuite," she is credited in the opening titles as Lieutenant Ezri Dax, not Lieutenant J.G.
Ezri is named as the station's counselor. For such a large station, having only one counselor would leave the staff and inhabitants underserved. It would be akin to only having one physician, when Julian has an entire staff at his disposal. Even stranger, the station spent 6 years as a Starfleet outpost without even a single counselor. Mental health in the 24th century Federation is usually taken more seriously than that, es evidenced by the ship's counselor being part of the senior staff onboard the Enterprise. Even aboard the USS Destiny, Ezri's post before becoming joined to the Dax symbiont, she was an assistant counselor, indicating the presence of a staff of mental health specialists.
In the episode Disaster (1991), it is established that Starfleet counselors are essentially trained psychiatrists and apparently hold an "honorary" rank of lieutenant commander. This would match modern day equivalents of military psychiatrists who are full MD doctors with a follow-up residency in psychiatry, the average time to obtain such a position being around 12 years of schooling. However, Ezri Dax is shown to have no such education and training as an Ensign and is far too young to have spent over a decade obtaining the required degrees and certifications for the position she holds.
Ezri says to Kira, "It's a strange sensation, dying. No matter how many times it happens to you, you never get used to it." A Trill symbiont must be removed from the host before death or the symbiont will die as well. Ezri would not have any memories of her previous hosts' deaths. At most she would have memories of being mortally wounded.
At her promotion celebration, Ezri asks Quark if Worf is there. Quark says, "Good question," and becomes uneasy (due to the threats against himself and Julian earlier in the infirmary). Worf is a very large man and the only Klingon in Starfleet, and the ward room is not that large. Worf is standing only a few meters away, in plain view. It is not possible that neither of them would have noticed him there.
After Ezri is promoted to Lieutenant and the others are applauding, Colonel Kira claps in the Terran fashion - palm to palm - rather than Bajoran style, with the back of one hand into the palm of the other.
In Quark's bar, Bashir, Odo, and O'Brien believe that Garak is taking notes on their costuming needs for their holosuite program, but it is revealed that he is actually working on decryptiing classified Cardassian intel for Starfleet. A seasoned intelligence operative like Garak would know not to have such delicate material out in the open.
After Garak is brought into the infirmary by Odo, Bashir and the others are informed that Garak's claustrophobia has worsened. Bashir says, "I wish I had an explanation, but I don't. He checks out fine." Claustrophobia is a psychological condition, not physical. It wouldn't be picked up on a medical scan.
Worf's lack of acceptance of the situation regarding Jadzia/Dax/Ezri shows a bizarre lack of understanding around the very nature of a joined Trill for someone who was married to one.
After Jake comments that Ezri is cute, Ben tells him, "She's also about 300 years too old for you." This echos his sentiments towards Jadzia and Julian in "Emissary." By that logic, Dax's new hosts would only be able to form relationships with other beings that are several centuries old, which would severely limit their prospects in ways counter to Trill culture, which forbids "re-association." Joined Trills are meant to form new relationships and gain new experiences to enrich their symbionts. Strangely, Ben had no such qualms about Jadzia becoming involved with Worf, who is also several centuries younger than the Dax symbiont.