Let's assume there's a high speed spaceship moving right relative to us, and it's carrying two light clocks. One of them is set up so that the bouncing light pulse is oriented horizontally, and in the other one the pulse moves vertically, relative to us. Also, connected to both clocks there's a multicolored indicator lightbulb that flashes red every time the pulse in the horizontal light touches a wall, and flashes blue every time the pulse in the vertical light touches a wall.
Now let's consider the horizontal clock as observed from our non-ship reference frame. Since the ship is moving right, when the light pulse moves right we will see the clock's right wall running away from it. The contrary will be observed when the pulse goes left: the clocks' left wall will run to meet the light pulse. This will cause one of the two trips of the light beam to be shorter than the other, so the indicator lightbulb will flash red, followed by a long wait, then flash twice in quick succession, then a long wait again, and so on.
Now, the vertical clock won't be affected by the ship's sideways motion, so we will perceive the blue pulses in the indicator to occur evenly, thus not coinciding with the red ones.
Furthermore, the horizontal clock being length-contracted in our reference frame, the discrepancies become even greater.
Now, someone on the ship won't observe any of these effects that result from the ship's motion, and should therefore see both of the light pulse's trips as taking the same time, which would apparently cause the red and blue light flashes to happen in prefect sync.
How is this discrepancy resolved?