As for a captain not landing in the first wave at Omaha, who can really say? We know that things got very mixed up very quickly on the run in, with boats from different waves surging ahead, or falling behind, not to mention landing on the wrong part of the beach. Whole boatloads got wiped out with no surviving witnesses. Who is to say that a capatin wasn't amongst the casualties?

Also, it's not clear from the film whether Miller's boat is actually one of the first ones to the beach. Certainly it looks like the first engaged by a certain machinegun, but we don't know whether the action had already begun elsewhere several minutes before.

The main inaccuracy with the landing scene is that the Americans are held up on the beach for about 15 minutes overall, instead of the hours that occured in history.

As to the SS time scale, again the film is not quite clear how many days have passed between the landing and Miller being given the mission. HQ's and supply dumps seem well established, and we know that Miller has been up country in the bocage charting minefields and so on.

Private Ryan refers to the dead Germans in the half tracks as "Recon, 2 SS". Well he could be wrong anyway, and we might be looking at the very advance guard of a division arriveing 5 or so days after the landing.