Hilarity Ensues: The obvious one here is that there is a huge conflict of interest in the Oleson's Mercantile being the only dry goods store in Hero Township (and hence, the only one that Walnut Grove-area families are able to get to easily) and its part-owner being the Schoolmarm. Nels tries to point this out but as usual, Mrs. Oleson shouts him into compliance.
I Told You So: Basically, what Nels (who, along with Laura, has rural, conservative values) tells his wife after the regional superintendent explains the true role of rural schools and having a curriculum appropriate to meet the needs of its local residents and economy, this after Mrs. Oleson wanted one more suitable for the big city, got her way and ended up falling flat on her face.
No Dress Code: Of course it did not mean that the kids were allowed to come to school naked or scantily clad, even by 1800s standards. But, as the regional superintendent explains and Nels makes sure his wife understands after he explains things to her farming families cannot afford to buy expensive uniforms and often their children come dressed in overalls and plaid shirts, if not in standard button-down shirts and suspenders. The school dress code is, hence, an unwritten rule where it is expected that children dress appropriately.
Running Gag: Willie is sent to the corner a record number of times this episode at least 10 times, and all but once by his own mother! While funny for all the minor things that Willie didn't do each time, a class bully was responsible it begins to foreshadow his growing discomfort and frustration with his own mother coddling him all the time.
In the end, it is inverted: Laura having been restored to her teaching job finally catches the bully tormenting Willie, and when Willie thinks he's been sent to the corner again Laura tells him he doesn't have to go, because she saw the bully commit his deed and sends him to the corner. Willie can't believe it!