Yesterday's Enterprise - S3-E15
Corrected entry: When Tasha Yar and company first exit Ten Forward in the alternate timeline, watch through the doors as they open. An extra can be seen stood still in midstride in the passageway, before nervously noticing that the doors have already opened and that she has missed her cue to begin walking past. She then begins purposefully marching down the passage.
Yesterday's Enterprise - S3-E15
Corrected entry: Throughout the episode, Lt. Richard Castillo wears a Type 2 phaser, which was seen in Star Trek II. He should wear the phaser introduced in Star Trek V, or any phaser consistent to the timeline. The movie [ST V] and the episode were shot in the same year. The old phaser is clearly visible in the sickbay scene at 18:18. (00:18:15)
Correction: You are assuming that when a new piece of equipment is issued, it immediately replaces older versions throughout Star Fleet. In the Star Trek Universe, it has been shown that these sorts of changes take time. For instance, in the original series, the Pilot-syle uniforms were seen as late as the second season. If an officer is used to a particular style of phaser, he may very well continue using it even if there is a newer version available.
Correction: I just watched this scene like 20 times and watched the entire episode to make sure it wasn't a similar scene. This doesn't happen.