When Mac walks into the courtroom one of her medals is falling off. In the close up Mac's medal is on correctly. Then a far show again her medal falling off again.
A framed certificate for the Purple Heart names the recipient as a "first lieutenant" - the rear admiral in Japan while he was a junior officer. "First lieutenant" is not a rank in the US Navy; the corresponding Naval rank is "lieutenant (junior grade)".
The opening scene is time-stamped at 1104 Zulu time. That is 2004 Japan time (Zulu +9) or 8:04 p.m. It is not said what month (though it is clearly not winter), but it is dark already, and that seems reasonable. But later there is a scene during a subsequent day which is time-stamped at 1057 Zulu (7:57 p.m. Japan time), which is only seven minutes sooner than the opening scene, and it is broad daylight. This is a glaring inconsistency.
Female officer in the background at the reception is wearing her tie incorrectly. It should be tucked under the lapels of the jacket, not visible on top.
While talking to Jun, Harm says, "Your eyes deceive you." Harm explained that he could see in her eyes that she wanted to tell him something, but was afraid to. That is, her claim not to remember the attack was false. But what he should have said was "Your eyes betray you."