Something that has been concerning me recently is what I perceive to be differences from Exodus, Leviticus, and Numbers vs Deuteronomy. Mostly this is regarding the Levites and the tithe.
Something I've noticed before: In the rebellion of Korah, Moses seems to make it clear that the Levites are not actually the priests (Num 16:9-10), yet in Dt 17:9, 17:18, 18:1, 24:8, etc it could be interpreted as referring to them as such. Of course, Aaron is a Levite, but the distinction is made quite clear between his family and the tribe at large in the preceding three books.
More obviously an issue (in my opinion) is the issue of the tithes and the Levites. Num 18:21 says all of the tithe is for the Levites and that they may eat it anywhere (Num 18:31). However, Dt 12:17-18 and 14:23 refers to eating the tithe and simply sharing some with the Levite in your gates, not giving it all to the Levites.
Same thing is said regarding firstborn and firstfruits in Dt 12 and 14, yet Dt 18 only refers to firstfruits being the levitical portion.
When Torah says "priests the Levites" it simply emphasizes that only the Priests can eat it. This is because every priest is a Levite but not every Levite is a priest (similar to - every Jew is Hebrew but not every Hebrew is a Jew). The phrase seem to be distinct to Deuteronomy.
I found Deut 12:26-27. Deuteronomy is questionable to me. I do not know how to equalize it with the rest of the Torah. Another thing I noticed that in Deut 12 and 14 it speaks to all congregation - not just the Levites, so maybe that is the case. But it does seem to explicitly contradict itself.
Regarding the firstborn/tithe/etc, we can compare it to the passover issue. I'm not sure what I think of the situation and don't reasonably know of a way to reconcile the Levitical portion contradiction. I do not think it is reasonable to assert that simply because it was shared with the Levites that this would fulfill what was required in Numbers, because they are supposed to be receiving it in full to be eaten where they wish. I haven't thought of any explanation that can actually resolve this.
Now, I did notice in Dt 18:4 that the firstfruits are said to belong to Levi, which was implied in Dt 12:16-17 as being eaten by the people in general. Not sure what to think of that exactly. I’ve checked the SP in a few places and noticed no significant variation. I checked the Septuagint, and it has a slightly varied wording but the issue is not changed. It says to "bring" the tithe, etc, to the place, which is absent from the Hebrew, and I initially thought maybe the rest would say differently and maybe say that "it will be eaten" (i.e., Levites shall eat it), but it still read similarly to the Hebrew otherwise (you shall eat). So no real answer there I guess.
Deuteronomy is indeed problematic. There are other issues as well if I remember correctly. For example, Deuteronomy provides different account of journeying of the Hebrews in the desert. And other minor things.
The journey description near the beginning of Deuteronomy seemed odd. I did compare it and thought it was arguable that it was able to be reconciled, but it was definitely odd how things were explained. For example, how it describes the Levites being separated seemed inconsistent with the timing and reason given in the preceding books. Same for the death of Aaron to some extent in that it seemed to be conveying that he died much earlier (if I remember correctly).
Unfortunately, all primary sources seem to match so there is no obvious way to reconcile it.