Inconsistencies
I'm just starting watching the complete series, but I watched much of it before so can name a few inconsistencies. I won't get heavily into historical inaccuracies or contradictions with the books or I might never get done. One of the biggest contradictions to the books is there is WAAAAAYYY more crying in the series, in situations in which the real people cried very little if at all. Laura was taught it was babyish to cry and may have even got in trouble for it. (Gotta read the books again.)
At the beginning of Season 1, it is made clear that Laura can't read or write. Her narration states, "If I had a memory book, I'd write (such and such)." A later episode is based around her keeping a memory book when they first arrived in Walnut Grove.
Season 1 makes several references to what was known as Custer's Last Stand, now politically correctly termed the Battle of the Little Bighorn. This took place June 25 and 26, 1876. So fine, Season 1 takes place after that. Only it doesn't, because in 1976 they did a big show celebrating America's Centennial in 1876, so these Season 1 references were to something that hadn't happened yet.
In Season 1, Doc Baker operates on Mrs. Oleson to remove her appendix. Later in the series, in the faith healer episode, the doctor insists a young boy get to a surgeon to have his appendix removed. Why can't Doc Baker perform the operation since he has already successfully done it at least once?
Of course the most famous one was that Albert returned 20 years later as a doctor, but a TV movie implied he died. I haven't seen this movie but understand it doesn't actually show him dying so there's hope.
I know married women were not allowed to teach, and I'm not sure even married men were. Teaching salaries were not enough to support a family, so married people were barred from teaching. There were also rules about being seen while pregnant, though those may have been more strict out east. These rules were broken by Mrs. Simms and Mrs. Garvey teaching and Mrs. Simms leaving class to give birth to a baby.
Two more episodes, two more inconsistencies. In "Survival," Charles says it's been 16 years since the 1862 uprising, implying it is 1878. About a year and a half later it was 1876. Time ran backwards...amazing. In "To See the World," Johnny Johnson ditches school. Later in the episode, he mentions it's July. There isn't school in July. The reason was both that kids were needed on the farm, and that school buildings became intolerably hot in summer. A three month vacation has been a tradition ever since.
As far as research being harder as back then there wasn't Google and all, as a child I was able to grab a World Book without getting out of my chair. I learned things such as: they played baseball, which was invented, but were using gloves, which weren't yet. Albert's pen pal claimed to captain the basketball team. Basketball wasn't invented until 1891 and I'm sure girls' teams started later. Football was also very new then and probably wasn't played on the prairie in the 1870s/1880s in the manner depicted on the show. I often wondered why the makers of a national TV show couldn't afford a set of World Book. These could go on all day and are probably found in every show, though some are more careful than others. (I understand Dr. Quinn was really pretty careful.) I just finished watching Daniel Boone, which was one of the worst offenders. It begins in 1775 and then bounces around in time so much between 1775 and 1807 (in only six years) that you'd think you were watching Quantum Leap. The main thing I kept track of was the music, and hope to list which pieces Daniel Boone could, and could not, have heard in his lifetime. I'm not doing this with Little House because although I recognized most of the fiddle tunes on Daniel Boone, I have recognized very few on Little House. I know Little House does use for instrumental background vintage tunes which weren't written yet back then.
In Season 2, episode 2, the eye doctor tells Mary she must wear her glasses at all times at first, and then only for schoolwork. In episode 3 she is at school without her glasses.