The level of alien medicine in Dr. Bashir's jar frequently goes up or down between shots. This is because the pills are actually just M&Ms, and actors would frequently steal them between takes, until the producers glued the jar shut.
When the Ferengi were introduced on Star Trek The Next Generation they are shown to have far superior strength to humans. They are portrayed as far weaker on Deep Space Nine.
In S1 E17 Major Kira switches from jacket and trousers to an all in one jumpsuit yet in several episodes she is suddenly wearing her light coloured top.
The naming convention for the landing pads on Deep Space Nine is inconsistent throughout the series, with characters sometimes using numbers and other times using letters.
In several episodes, Bajor is depicted as having several moons with apparently normal atmospheres and gravity. But if the moons were that large/dense/massive, they would not simply be orbiting Bajor. Bajor and the moons would be orbiting each other in a kind of cluster, which might have resulted in occasional collisions in the past.
A type of mystical artifact recurs throughout the show referred to as "orbs" (The Orb of the Prophets, the Orb of Time, etc.). Orbs are, by definition, spherical. The items referred to as "orbs" are almost hourglass shaped, with bulbous ends and a tapered center.
In every external shot of DS9, there are no ships docked anywhere, yet the plot involves visiting vessels that should appear in external shots during the episode.
The drink Kanar; We see several different people pouring Kanar into glasses throughout the series, both Cardassians and Quark. The liquid we see varies from a thin pink fluid in one episode to a thick dark fluid that almost looks like molasses in another, to a whiskey like liquid in a later episode. However, many Earth drinks have different colors and consistencies. Rum, for example, comes in clear and dark coloration. Tea comes in over 3000 varieties, with variations in color. Milkshakes comes in various colors and consistencies depending on the ingredients used, from a thin water-like consistency to one as thick as ice-cream.
During the opening title sequence, the wormhole is shown at inconsistent angles to how it looks as the crew observe it from the station's windows. In the title sequence, the wormhole is angled upward at approximately a 40° angle. When the crew observes it from the station, it's pointed down at about a 260° angle. However, it must be remembered not only is there no "up" or "down" in space, but also that the DS9 station is mobile. It is transportable via thrusters and so can be repositioned at any angle around the wormhole by the crew for whatever purpose they see fit.
During the Intro Sequence from Season 4 onward the Defiant Model is different from the rest of the series, the bridge section is lower than it is during the series, when it should be above the main section.
Throughout the series, sometimes the comm badge emits a tone when pressed, sometimes it does not.
In the first three seasons, CDR Sisko refers to his father in the past tense, even talking about his slow demise and death from some unknown ailment. But starting in the fourth season ("Homefront"), Joseph Sisko is alive and well running a restaurant in New Orleans. Joseph appears in a total of six episodes throughout the last 4 seasons.
Several times, Starfleet or Bajoran military characters remove their comm badges to avoid location by the station computer. However, in one episode, Sisko uses the computer to find Jake, which means it must have a secondary location algorithm that, for some reason, never kicks in when it would be inconvenient to the plot.
The number of Dax hosts Jadzia and Ezri state there have been, fluctuates throughout the series and is usually inaccurate. After Verad became another host in a season 2 episode, and Joran was acknowledged to be a previously-missing host in a season 3 episode, there are 10 hosts in all: Ezri is the tenth, and after Joran and Verad are counted Jadzia is the ninth. Yet Ezri in her only season (7) states she is the eighth, and Jadzia after season 3 usually states SHE is the eighth (counting Joran but forgetting about Verad), though before Joran was discovered (season 3) but after Verad (season 2), Jadzia still says she is the eighth (she counts Verad).
A number of times throughout the series when Odo changes shape or reverts to his liquid state his combadge ripples and turns to a liquid along with the rest of his body. However unlike his "clothes" the combadge is a piece of technology, not a part of his body like his uniform is. So when Odo changes shape or becomes a liquid his combadge should either fall off, or be pulled into his liquid body. It wouldn't ripple and turn into a liquid the way his uniform does.
Although the Federation and Starfleet use the metric system, there are numerous occasions when the ship's personnel refer to distances and capacities in obsolete units such as feet, miles, pounds, etcetera.