I think it's fine that Duolingo accepts "than him" but I would prefer Duolingo not tell me that "We are going to read more books than him." is "another correct solution" because it not really correct in English. (It's okay to be sloppy but sad not to know what the correct grammar is.)
Both vjmoore and karimagon are correct. It's a perfect example of the evolution of language. What was once considered proper grammar has eroded in common use to the point where it eventually sounds odd to most people's ears and begins to detract from the clear understanding of language. Eventually the old rule is dropped even by the official academic keepers of the language. I think that this phenomenon has existed in all times and with all languages, but is accelerating due to the ubiquity of person to person textual communication in the digital age.
The whole point of using "I" or "he" in this situation is to eliminate ambiguity and I wish people would use it exclusively. It doesn't sound odd if you add "is" at the end, e.g. "I am taller than he is," etc. which is what I do. In that situation, saying "him" wouldn't be ambiguous (just incorrect/sloppy grammar in my opinion), but it IS ambiguous when you say, for example (another sentence on DL), "I love you more than her" because technically that means "I love you more than I love her" but people will also use it to mean "I love you more than she loves you", which is obviously the clearer way to say it.
Those are some good points, but I doubt the genie can be put back in the bottle, especially since the majority of the reading many young people do today is reading text messages, wherein the worst grammar possible is being made to seem normal. It would take a major initiative on the part of the entire educational establishment to even slightly turn upcoming generations back toward proper grammar. The battle for the restoration of proper grammar seems all but lost.
The point of language, and of its grammatical rules, is correct and clear communication. Because language is mutable, these rules change over time, along with the general consensus and understanding of what they mean. While technically correct grammar may be important in, say, an academic setting (and I would argue that DuoLingo is a mild academic setting), in casual conversation, the only thing that really matters is mutual intelligibility. As such, while the examples you gave of grammatically confusing sentences are very good examples of instances wherein this specific rule becomes important, I would posit that it ceases to be important in situations with less ambiguity. It's like the dangling preposition, in that it may have been incorrect once upon a long time ago, but now, it's pretty archaic.
Besides, technically correct grammar doesn't even always avoid ambiguity. Don't get me started on the word "inflammable."
Because they don't allow the correct word "he" in the section where you choose boxes, I can't complete the lesson and am forced to test out of the entire section. Please, DL, if you insist on allowing "him," at least include "he" as a choice here, so we aren't required to choose an incorrect word in order to avoid ditching the entire lesson.
Can't find the when to use " ú " with accent and not to use "u " without accent, ex. que(?)
How does one know when to hear this phrase as "Let's read more books than him"?? I know better than to input this answer into Duolingo but I am pretty sure this can be heard as a suggestion. In fact, I have a hard time not hearing it that way. There's something about the word "vamos" in my mind that makes it feel almost little more like a command in the nosotros form but I not sure if it just me. In fact, this is consistent with the fact that the actual command form "vamonos" has taken on the feel of "let's get outta here" leaving the "vamos" to serve double duty. Help me out here, especially if you are native.