When Spock moves to kiss La'an at the end, he tilts his head to the right, but the camera angle changes and his head is tilted to the left for the rest of the kiss.
Until minute 2, Kirk wears his hair parted on the right side, and his trademark curl falls to the left. In the following scenes, it is exactly the opposite, corresponding to the original.
The opening post-credits scene shows the Enterprise in front of the neutron star it is studying. The lines of the star's magnetic fields are clearly visible, however they should not be. Since this is an "outside" view of the star and the Enterprise, and not a sensor image seen on a screen, those lines would not be present as they cannot be seen by the naked eye. Just as the magnetic fields of the Earth and the Sun are not visible to the naked eye. A neutron star does have a vastly more powerful magnetic field, anywhere between a billion to a quadrillion times that of the Sun's, as such it is theorized the field lines might be visible to the naked eye when interacting with charged particles like from gases in a nebula, but this star is not in a nebula.
Where was the real Mr. Spock during the time the Enterprise was studying the neutron star? Shouldn't he be on the bridge at the science station observing the event.
The real Mr. Spock should have been at the science station on the bridge during the time the Enterprise was studying the neutron star. There was no mention of where he was during that time.
La'an doesn't ask for the computer to add an assistant to the holodeck story until after two people had already died. Spock couldn't have been the killer.