Oh, yes... the exact content of American history texts (and those of other subjects) is certainly open for improvement... I found myself correcting my teachers from time to time even in 5th grade concerning the presence of mis-information in the texts.
The claim that "everyone at the time of Christopher Columbus thought the world was flat" was one... the reality being that most educated people (including the various nobles CC tried to get financing from) were well aware that the world was round.
They were opposed to his plan because they believed it was of larger diameter than CC did, and that therefore he couldn't make it all the way to the Indies islands (now called the East Indies).
Of course, they were right... his calculations were well short, and if the Americas hadn't been in the way his entire expedition would have starved before coming anywhere near land. He was lucky, not right.
Most of the issues like you mention are due to lazy and inattentive students, however, as they are taught mostly correct facts... they just don't remember then accurately (if they learned them in the first place)..
And yes... the only major battle the US won in the War of 1812 was fought after the treaty ending the war had been signed (New Orleans). Most of the treaty confirmed the British position... but the US did get its own rights confirmed, and a promise by Britain to be more careful in applying its rights.