General concepts in Japanese (that it took me an embarassing amount of time to understand)
It's truly amazing the number of things that seem obvious to intermediate learners but will puzzle you to no end when you're starting.
I'll try to put all these "fun facts" here so that someone else doesn't spend as much time as I did trying to understand these things!
There is no rules to romaji
Or more accurately, there are multiple ones. For example, you'll see 学生 romanized as gakusei in most places, but some books like Genki use gakusee. One more reason to ditch romani as soon as possible.
No all letters are actually pronounced the way the romani will make you believe they should
Related to previous point: the い after a え sound is actually much closer to a long え than it is to えい (think "hey").
Similarly the う after a お sound sounds like a long お.
In syllables that end with a consonant and then a う (つ for example), the う is barely pronounced before certain consonants like k-sounds but is pronounced before others like b-sounds.
>> That's why つばさ (翼, wing) is pronounced "tsubasa" while つき (月, moon) is really pronounced "tski".
Kun'yomi readings and on'yomi readings (and why I don't care)
Each kanji has at least one kun'yomi reading and one on'yomi reading. The kun'yomi is the Japanese reading, and the on'yomi is the Chinese one (or at least how they translated the Chinese sound).
I haven't so far found a reason to learn which reading is which - I'd rather learn by vocabulary. The kun'yomi reading is the one used when the word is a mix of kanji and kana, while the on'yomi is the one used most frequently when the word is only made up of kanji.