These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Mostly because it becomes an argument of "What Would YOU do?" It's easy to say what you would do in that situation, and the internet (and real life, for that matter) are chock full of people who will disagree with you, whatever your claim may be.
Dawson Casting: Sort of. By the time of Normandy, most officers (in battle and combat) were in their late twenties to early thirties at most, with everyone under them being younger, even if only by a couple years. Tom Hanks was in his early 40s when this was filmed. All of the other actors were (for the most part) older than their characters, save Horvath (whose relative age is left untouched entirely).
Fanon: Many people who saw the film were confused as to whether the German soldier that kills Corporal Mellish is also "Steamboat Willie." They are in fact, different soldiers. The soldier that kills Mellish has Waffen SS lapel insignia, while "Steamboat Willie" has the lapel insignia of an enlisted soldier in the Wehrmacht Heer. It doesn't really matter what you yourself think - if they were the same person it adds a little interesting twist, and if you felt bad for "Steamboat Willie" you can feel he survived the war.
If you go along with the idea that they're the same guy, it adds a layer of harshness considering that it was Upham who defended him at the radar station. Then he returns and...
Except that we KNOW Steamboat Willie doesn't survive. He's right there among the PO Ws before Upham, and after a brief exchange in German, recognizes the one of two Americans who has shown him mercy. He gives a softened, defanged, and almost pitiful "Upham!", outright recognizing and in the same moment attempting to appeal to the one US soldier he ever connected with personally. And then Upham fires. Granted, the shot is done so that we don't actually SEE who he fires at, but instead of remaining ambiguous, the film shows the remaining Germans present...and there's Steamboat Willie. With his face in the dirt. And dead.
Hell Is That Noise: The approaching German Tiger as the American soldiers were getting ready.
Misaimed Fandom: As discussed on the main page, many ignore the message that War Is Hell and only like the carnage on the war scenes.
Retroactive Recognition: A lot of the younger actors, especially Matt Damon and Vin Diesel, were not yet megastars at the time this movie came out. Matt Damon had won an Oscar (albeit for Best Screenplay), but it may yet have been a flash in the pan. Spielberg is rightfully credited as helping jump-starting Diesel's career, writing the role specifically for him after seeing Diesel in his acclaimed short film.
Jeremy Davies (Cpl. Upham) is Daniel Faraday in LOST.
Nathan Filion as Private James Ryan #1 ("James Frederick Ryan, Minnesota.")
Paul Giamatti and Bryan Cranston also have small roles and went on to become acclaimed actors.
Seinfeld Is Unfunny: Both on the giving (it's not the first movie to use a documentary-like depiction of war or realistic carnage, but the first popular one) and receiving ends (the influence on war movies or battle scenes in general, complaints about the patriotic\emotional tone of the scenes after Omaha Beach).