During her chess-type game with La Forge, Guinan makes two moves in a row (La Forge not playing in between). Also, the number, shape and position of chess pieces on the top level keeps changing between shots.
In the opening scene, where Captain Picard and Geordie discuss the arrival of Dr Brahms, it is apparent that Captain Picard was unaware of her previous assistance (as a hologram recreation in the holodeck). Her "virtual" assistance basically saved the Enterprise, in the episode "Booby Trap." This was a dramatic, very significant, encounter which the captain should not have forgotten.
Worf describes the galactic child as occupying a volume of 46 million cubic meters. A cube that size would be more than half the length of the Enterprise in width, height, and depth. The child is clearly much smaller than that.
The way the 21cm hydrogen line is discussed has no relation to it's real meaning in astronomy. The line shows up in frequently observed in radio astronomy not because everything vibrates at that frequency (a complete nonsense) but because hydrogen is the most common element in the universe and this wavelength passes through many things easily.
When Leah Brahms is on the holodeck berating Geordi over his use of her likeness, most of the shots use a frozen image of her on a split screen so she can appear as both herself and the paused hologram. A couple of shots, in which the holographic version is only seen from behind, use a body double dressed in the hologram's outfit and hairstyle, and the body double can be seen moving slightly.
The creature covers shuttle bay 3 when latching onto the hull. The crew then repeatedly references it covering shuttle bay 2 and how they should decompress shuttle bay 2 to remove the creature from the hull. Visuals then show shuttle bay 2 being decompressed. The creature is not over shuttle bay 2. It's clearly positioned over shuttle bay 3.
In the shots where the mother creature is attacking the Enterprise, there are no lights in any of the windows, before, during, or after the attack. The lights remain on in all interior shots, so it's not a matter of the creature's attack draining power and shutting off the lights. Likely the effects team was in a rush and didn't have time to properly light the model.
When Picard is off the bridge, Riker is seen sitting in the first officer's chair. Whoever is in command of the ship should sit in the captain's chair.
After Dr. Brahms beams in, Geordi's first word to her is, "Hi," but his lips do not move.
There is no clear reason for Geordi not to be upfront with Leah on how he came to know her. Several opportunities present themselves, but Geordi avoids them and instead comes across as a grinning creep constantly trying to make a strong personal connection. When Leah discovers her holodeck recreation and accuses Geordi of making a fantasy sexual playmate of her, he swiftly throws the matter of wrongful behavior back onto her by saying he just wanted to be her friend, cementing him as a creep AND a non-gentleman.
In Ten Forward, Geordi describes Dr. Brahms as unfriendly and too focused on her work, and says that she hates what he's done to her engines; yet, in their previous scene together, Brahms expresses admiration for one of Geordi's modifications, to the point of encouraging him to publish a paper.
Upon first encountering the space-faring creature, Data mentions that nothing like it has been encountered before or observed on record. While it is true that this particular creature may have not been observed before, it should be noted that the Enterprise did encounter another space-faring creature quite similar to this one a year prior in Tin Man (1990), and yet no mention of it is made here.