A few of those can be explained away.
* nuChekov could have been born earlier than in the Prime Universe because of the attack on the Kelvin. Chaos Theory
allows that one thing could affect many other things.
* Riker was referring to a setting of "Level 17" which would obviously be more powerful both in intensity and technological wise to the TOS phasers. Also, using a setting that could bring down "half a building" would be a pretty dumb thing to do in a cave.
*It's long been known that TAS isn't considered canon.
* All the pulses would have the exact same modulation because Data programed them in all three time periods. Since present Data's reading showed three identical pulses, it logically follows that those pulses would have come from the same source, and Data even prefaces the statement with "It's as if..."
* "Future Guy" was messing with the timeline, so something he told the Sulibon to do obviously prevented the war that Picard spoke of. Again, chaos theory allows for this.
* D7's were retired decades ago. Those could be D15 or so. The Federation used Excelsior class ships in the 24th century. Surely a scan would reveal them to be much more advanced than the one captained by Sulu.
The rest were errors. As for the video, it is very well put together. Very good job!