When Burnham enters the transporter room after Saru has programmed the transporter to take him to Kaminar, in one shot her phaser is holstered backwards.
When searching the sphere data for information on Kaminar, the print of the display between Burnham and Tilly is forward when seen from the front or back.
When Saru beamed down to the planet after being asked to leave the Bridge by Pike, he set the timer on the transporter for 1 minute from the time he set it to when the transporter would beam him down. However, the amount of time that passed between him setting the timer to the time he beamed down was only 50 seconds. Clearly not 1 minute.
When the crew of Discovery is tracking the historical populations of the Ba'ul, unevolved Kelpians, and evolved Kelpians, at one point the number of unevolved Kelpians drops to 0. Unevolved Kelpians are just members of the Kelpian species who haven't yet undergone Vahar'ai, a process of advanced physical maturation. In other words, all young Kelpians are in the "unevolved" category, with many remaining so well into what most species would consider old age. By this reasoning, all Kelpiens must have reached this point of maturity and none were born at all for a significant time period, likely many decades, which would be impossible for the propagation of the species.
When Saru is captive on the Ba'ul ship, another Kelpian is transported in. Saru is able to identify the form as his sister when it is still a formless blob of light, before she materializes.
Whilst Saru is chained to the wall his left restraint comes free as he is trying to free himself. The picture then cuts away but when it returns to him the restraint is closed again.
Saru programs the transporter to take him to Kaminar on a 60-second delay. The transporter activates 47 seconds later.
Commander Saru managed to open his left shackle after the Ba'ul left him in the chamber. When the drones enter the room, his left shackle is locked again.
When Paul Stamets and Dr. Pollard are discussing Hugh Culbert's status and scar the scene ends with a small lenseflare at the bottom of the screen over Stamets' torso. When the camera pans to the right a hand holding a flashlight is briefly visible. This is obviously a crewman's hand holding the light to create a lenseflare effect.
Commander Saru should not have been able to beam down to the planet surface during the initial confrontation with the Ba'ul; the Discovery was at Red Alert and her shields were raised. It has long been established in Star Trek canon that a transporter cannot be used while a vessel's shields are up as the transporter beam would be blocked by them.
Despite the Kelpiens being very sensitive and fearful, Siranna's threat ganglias don't seem to activate at some points where they most certainly would have to, especially when Michael appears to her (she never saw anything other than Kelpiens), and when she is in the Ba'ul structure, including when the Ba'ul and the drones are threatening them and Siranna looks terrified.
When Saru is ordered off the bridge, he enters the turbolift and it takes him to another deck without him ever giving it a destination.
A good portion of the Discovery's hull was eaten away by spores in Saints of Imperfection (2019), yet the ship appears pristine without ever having gone to spacedock for repairs.
The Ba'ul are said to have only developed warp drive a couple of decades earlier, putting them nearly 200 years behind Starfleet, technologically. Their ships should pose no threat whatsoever to Discovery.