I have decided to cover all the technical terms possible. The grammar section is lacking but this is otherwise a thorough list.
Character composition (造字 (zouji))
Bushu (部首): A radical, a component of a Chinese character by which it can be classified.
Ifu (意符): The semantic component of a kanji, indicating its context.
Onpu (音符): The phonetic component of a kanji, indicating its reading.
Hen (偏): Left-half radical, e.g. 行人偏 (gyouninben, "a radical similar to the person radical that appears in the gyou character").
Tsukuri (旁): Right-half radical, e.g. 彡旁 (sandzukuri, "a radical similar to the three radical that appears on the right side of a character"). On a technical note, there is no three radical, just character 😛
Kanmuri (冠): Top radical, e.g. 鍋蓋 (nabebuta, "\"lid\" radical").
Ashi (脚): Bottom radical, e.g. 二十脚 (nijuuashi, "a radical that looks like the kanji for \"twenty\"").
Tare (垂): Top-left radical, e.g. 屍 (shikabane, "\"corpse\" radical").
Nyou (繞): Bottom-left radical, e.g. 之繞 (shinnyou, "the most common nyou radical, appearing in the kanji for \"advance\" and countless more..."),
Kamae (構): Enclosing radical, e.g. 門構 (mongamae, "\"gate\" radical").
Hane (跳ね): A stroke that ends in a "hook", e.g. 亅 (hanebou, "\"hook\" radical").
Tome (止め): A stroke that ends as a line, e.g. 丨 (bou, "\"line\" radical").
Harai (払い): A stroke that ends in a curve, e.g. 丿 (no, "\"bend\" radical").
Rikusho (六書): The six categories of kanji construction.
Shoukei (象形): Pictogram, representing a picture, e.g. 傘 (kasa, "umbrella").
Shiji (指事): Ideogram, representing an idea, e.g. 三 (san, "three").
Keisei (形声): Phonosemantic compound, where one component represents the context and the other the reading, e.g. 狐 (-ko-, "fox"), from 犬 (inu, "dog") and 瓜 (-ka-, "melon")..
Kaii (会意): Compound ideograph, where two ideographs form a character, e.g. 囚 (-shuu-, "prisoner"), from 囗 (kunigamae, "enclosure") and 人 (hito, "person").
Tenchuu (転注): A mysterious category, "derivative cognates", where a character splits to form two similar characters, e.g. 考 (-kou-, "thought") and 老 (-rou-, "old age"). Note that 孝 (-kou-, "filial piety") is not a derivative cognate, but rather a phonosemantic compound, where 老 (-rou-, "old age") is the phonetic component and 子 (ko, "child") is the semantic component.
Kasha (仮借): Phonetic loan, where a character is used to spell an unrelated term, and the original meaning of that character is often then represented by an altered version of that character, e.g. 求 (motomeru, "request"), whose original meaning is now represented by the phonosemantic compound 裘 (kawagoromo, "fur coat"), by addition of 衣 (koromo, "garment").
Eijihappou (永字八法): The eight most basic strokes of the character 永 (ei, "eternity"). In order, their names are 側 (soku), 勒 (roku), 努 (do), 趯 (teki), 策 (saku), 掠 (ryaku), 啄 (taku), and 磔 (taku).
Grammar (文法 (bunpou))
I (い): Adjectives with the titular suffix.
Na (な): Adjectives with the titular suffix.
Tari (たり): An archaic class of adjectives with the titular suffix.
Ichidan (一段): -iru/-eru verbs.
Godan (五段): Non-iru/-eru verbs.
Yodan (四段): An obsolete class of verbs, superseded by godan in modern Japanese.
Nidan (二段): An obsolete class of verbs, superseded by ichidan in modern Japanese.
Readings (読み (yomi))
Gikun (義訓): An instructed nonstandard reading of a kanji in a given text.
Goon (呉音): A common class of on'yomi, earlier than kan'on, named after the Wu region, often used in Buddhism and ancient times, e.g. 勿 (-mochi-, "do not").
Ijidoukun (異字同訓): A kun'yomi that has nuances depending on the kanji with which it is written. Example: 赤い (akai, "red"), 紅い (akai, "crimson").
Jukujikun (熟字訓): A special kun'yomi that is attached to multiple characters rather than any single character. This most often occurs when a spelling consisting of two or more characters is borrowed from Chinese, but the native Japanese term is applied, resulting in an irregular reading. Example: 蜘蛛 (kumo, "spider").
Juubakoyomi (重箱読み): On-kun reading pattern, as in the titular term.
Kan'on (漢音): The most common class of on'yomi, later than goon, named after the Han dynasty, e.g. 勿 (-butsu-, "do not").
Kan'youon (慣用音): Customary on'yomi.
Kokkun (国訓): A kun'yomi that differs from the original Chinese meaning. Example: 鮎 (ayu, "sweetfish"), whose Chinese meaning is "catfish".
Kun'yomi (訓読み): The Japanese translation of the meaning of a Chinese character, applied to that character as a reading. Kun'yomi are basic words.
Nanori (名乗り): A reading that is used exclusively in names. Note that regular kun'yomi and on'yomi may be used in names too.
On'yomi (音読み): The Japanese representation of the sound of a Chinese character. On'yomi are technical roots.
Rendaku (連濁): Sequential voicing. 赤狐 (akagitsune, "red fox") comes from 赤 (aka, "red") + 狐 (kitsune, "fox"), but kitsune changes to gitsune.
Renjou (連声): Sequential nasal gemination, 天皇 (tennou, "emperor") comes from 天 (ten, "heaven") + 皇 (ou, "emperor"), but "ou" changes to "nou".
Souon (宋音): An extremely rare class of on'yomi, later than touon, named after the Song dynasty, e.g. 白 (-pai-, "white").
Touon (唐音): A rare class of on'yomi, later than kan'on, named after the Tang dynasty, e.g. 子 (-su-, "nominalisation suffix").
Yutouyomi (湯桶読み): Kun-on reading pattern, as in the titular term.
Script (文字 (moji))
Ateji (当て字): Kanji used to spell out a word phonetically. Example: 亜米利加 (amerika, written in kanji) instead of アメリカ (amerika, written in katakana). 米 is used for "me" even though it is read as "mei", but sometimes ateji take phonetic liberties.
Furigana (振り仮名): Transcription of the readings of kanji into kana in a text. They often appear above the kanji. They help you read the kanji and learn how to read them. Content whose target audience includes children is rife with furigana, and encylopedias introduce a topic with furigana.
Dakuten (濁点): Voice mark. か (ka) > が (ga).
Handakuten (半濁点): "P" sound mark. は (ha) > ぱ (pa).
Hatsuon (撥音): The ん (n) sound.
Hiragana (平仮名): The curvy phonetic script of Japanese, used by default.
Hyougaiji (表外字): A kanji that is marked neither as jouyou nor jinmeiyou.
Jinmeiyou (人名用): A classification of kanji that marks it as usable in names, in extension to the jouyou kanji, which may also be used in names.
Jouyou (常用): A classification of kanji that marks it as a kanji to be taught in education and acceptable for use in certain official publications and broadcasts. For each kanji, certain readings are marked as jouyou. The reason why Japanese uses fewer characters than Chinese is because Japanese applies two types of readings to each character, kun'yomi and on'yomi, thus making each character more complex in practise.
Kakikae (書き換え): Replacing a complex kanji with a simpler one with the same reading. Example: 才 (-sai, "counter for years of age"), whose standard spelling is 歳.
Kana (仮名): The two phonetic scripts of Japanese, hiragana and katakana.
Kanji (漢字): A Chinese character.
Katakana (片仮名): The blocky phonetic script of Japanese, used for loanwords or emphasis.
Kokuji (国字): A Japanese-made kanji, e.g. 凧 (tako, "kite").
Kyuujitai (旧字体): A Japanese traditional character.
Okurigana (送り仮名): Kana suffixed to a kanji indicating inflection. Okurigana used for the conjunctive form of verbs are sometimes omitted in set terms.
Mazegaki (交ぜ書き): Writing a kanji compound partly in kana. Example: 宝くじ (takarakuji, "lottery"), whose full kanji spelling is 宝籤.
Ryakuji (略字): An unofficial simplification of a character in writing, literally "abbreviated character".
Shinjitai (新字体): A Japanese simplified character. Japanese has only the most frequently used characters simplified, thus theoretically being closer to traditional Chinese, but in practise, not being so difficult to write. Unlike simplified Chinese, Japanese does not consider abbreviating repeated dots as a line in writing to be a part of the typeface of the characters.
Sokuon (促音): Gemination (っ or ッ). Gemination is the result of abbreviating bimoraic on'yomi in certain compounds, such as 窒素 (chisso, "nitrogen"), which comes from 窒 (chitsu, "obstruction") + 素 (so, "element"), but chitsu changes to chiQ. The reason why a lot of bimoraic on'yomi end in "u" is because "u" is the neutral vowel in Japanese that is used at the end of gairaigo (you wouldn't be able to tell this if you knew Mandarin, but non-Mandarin topolects have finals like t and k). Gemination is also used for emphasis in Japanese, especially in speech.
Sutegana (捨て仮名): Small kana. Example: ぁ.
Youon (拗音): -y- sounds, such as kya.
Vocabulary (語彙 (goi))
Gairaigo (外来語): A foreign word borrowed into Japanese. Usually, it refers to non-Chinese loanwords. Example: コーヒー (koohii, "coffee").
Godoku (誤読): A misreading.
Goji (誤字): A kanji misspelling.
Hyakushouyomi (百姓読み): Literally "peasant reading", misreading a kanji by hypercorrectly reading it by its phonetic component.
Jukugo (熟語): A kanji compound, e.g. the titular term.
Kango (漢語): A Chinese word borrowed into Japanese. Example: 世界 (sekai, "world").
Makura kotoba (枕詞): Literally "pillow word", an introductory epithet in Japanese poetry.
Nandoku (難読): (Of characters) difficult to read.
Nango (難語): A difficult word.
Nanji (難字): A difficult character.
Nyoubou kotoba (女房言葉): A cant of ladies-in-waiting, which has entered the general language.
Wago (和語): Synonym of Yamato kotoba.
Wasei eigo (和製英語): A Japanese pseudo-anglicism. Example: パンティストッキング (pantisutokkingu, "tights, pantyhose"), from パンティ (panti, "panties") + ストッキング (sutokkingu, "stocking").
Wasei kango (和製漢語): A Japanese-made on'yomi compound.
Yamato kotoba (大和言葉): A native Japanese term. Example: 世 (yo, "world").
Yojijukugo (四字熟語): A four-character idiom.