For about 1/2 of the episode, Castillo is missing his combadge on his uniform. Even after he changes out of his dirty/damaged one from the beginning.
In the closing scene where Guinan speaks with Geordi, Geordi is still wearing the uniform from the alternate time-line with closed collar and black insignia on the cuffs. Having restored the time-line at this point, his uniform should have reverted to standard.
While Yar and Castillo are in Ten Forward, Picard makes an announcement on the ship's public address system that senior officers will report to his ready room immediately. Later, Yar herself is there, who holds the rank of lieutenant. The ranks of lieutenant commander, commander, and captain would qualify as senior officers. With that, Picard should have said all senior officers and the chief of security.
Capt. Picard receives a communique addressed to "Capt. J.L. Picard." As "Jean-Luc" is hyphenated and therefore one word, "J. Picard" would be correct. This is either an error or else hints at a heretofore unknown middle name, e.g. Jean-Luc L. Picard. The same error occurs in the opening scene of Star Trek: First Contact (1996).
Captain Picard is stunned to hear that children should be on the Enterprise. But Wesley is still part of the crew in the alternate time line, although he was only on the Enterprise as a family member to begin with. In the altered time line, Wesley is on the ship as an officer, wearing a full Ensign's uniform in Command red, rather than his Acting Ensign's "uniform" as seen in the unchanged time line. He would be too young to hold this rank in the unchanged time line, but, in desperate wartime, age requirements can plummet.
The Klingon birds of prey's wings were in cruise configuration, not attack mode.
For some reason, the uniforms worn by the senior officers on the Enterprise C do not have the turtleneck undershirts or the belts with the belt buckles, but they have belt loops as seen from behind. However, the crew members wearing the uniforms with the beige shoulders, presumably junior officers, are dressed more stylishly with the turtlenecks and belts.
When Crusher calls to beam herself and Garrett to sickbay on the Enterprise D, Garrett is still sitting in her command chair when she dematerializes. Hopefully, the transporter will allow her to arrive standing up or laying down on a gurney since she has internal injuries. She does not need to materialize in a seated position and then fall to the floor.
When the Enterprise-C appears and alters history, the changes that happened are simple (e.g., uniforms, Worf, and lack of children). Later on, Picard tells Captain Garrett of Enterprise-C that the Federation is on the verge of losing the war. Considering that the war with the Klingons started over 20 years ago and continued in this alternate universe, one would expect that the Enterprise-D would look less like an explorer ship and more like a warship. If the Federation had been constantly at war since before the Enterprise-D, then the Federation would have redesigned their ships since you'd want fewer crewmen on a ship to die and more in individual ships to fight. As it is, the Enterprise wasn't changed and it was too big to be a fighting ship. One possibility is that the Enterprise-D was a planet-conquering ship, but that would only be the case when the ship is acting as a landing party and not a warship.
When Picard holds the meeting with his senior officers, he does so by squashing everyone into his ready room instead of availing himself of the more spacious conference room.
Just before the Enterprise-C enters the rift to go back to their time 22 years previous, the Enterprise-D is taking fire from the Klingons. A dark bar indicative of a dolly arm shadow can be seen passing from port to starboard on the Enterprise's surface.
When Guinan is sitting across from Worf in Ten-Forward, her glass of prune juice shows the reflection of the camera lens.
In times of war, many people get killed including command personnel, causing lower ranking officers to be promoted quickly. It is therefore inconceivable for Riker, LaForge, and Data to all still be serving on the Enterprise under Picard. They would most likely have commands of their own. Even Yar would probably at be a first officer under one of them, or on another ship.
It is almost impossible to believe that during a 20 year war with the Klingon's that the Federation never developed a cloaking device of their own. The Romulan's are not even a factor in the war so kicking the treaty of Algeron to the side shouldn't be that big of a deal in order to get an edge with the Klingon's.
When Data says "Nothing I have seen before" during the scan of the temporal rift, the tip of the microphone comes into view above Captain Picard's head.
When Commander Riker and Lt. Yar are performing repairs on the bridge of the Enterprise-C, Tasha refers to Geordi as Lieutenant. In later scenes, particularly the Ready Room briefing, it is clear that Geordi is wearing the rank of Lieutenant Commander, not simply Lieutenant.
After taking Tasha Yar's order, Guinan never returns with it. As she leaves, Guinan can be seen, apparently waiting tables.
When Dr. Crusher taps her badge and calls for transportation for herself and Captain Garrett, she puts her tricorder away and reaches up to tap her badge again and then reaches at the last moment to touch Captain Garrett, which would indicate to the transporter which person was to be beamed with her. She visibly catches herself before reaching to touch Garrett, and appears embarrassed at the slip.
Tasha Yar tells Lt. Castillo that the Enterprise-D is the first Galaxy-class starship. Federation naming convention (like in real life) is that the class is named after the first ship of its class. Hence, the first Galaxy-class starship would be the U.S.S. Galaxy.
Picard orders Enterprise-D to remain within 200 kilometers of Enterprise-C, to protect the "C" as it re-enters the rift. The visual immediately after his order shows the ships in close proximity, less than 1 km apart. 200 km (about 120 miles) is a ridiculous separation for one ship intending to defend another from multiple attackers.