Lit More Candles Than He Should Have
1. If one mistakenly lit more candles than he should have, e.g., two candles on the first night or four candles on the third night, some say he did not fulfill the mehadrin manner of lighting. [This commonly happens when one mistakenly lights the number of candles he prepared for Motzei Shabbos on Erev Shabbos.] They hold the reason we add a candle each night is to indicate which night it is; if one lit too many, there is no way to tell which night it is. According to this, he would need to extinguish all the candles and relight the correct number of candles (שו"ת אהל משה ח"ב סי' ס"ט ).
2. However, most poskim say bedieved he fulfilled the mehadrin manner of lighting, so he should only extinguish the extra candle (שו”ת אלף לך שלמה סי' ש"פ, מו"ר בשו"ת שבט הקהתי ח"ג סי' ר"ח ). On Friday night he may not extinguish it, but he still fulfilled the mehadrin manner of lighting.
Lit Fewer Candles Than He Should Have
3. One candle on the second night. If one lit one candle on the second night [or any of the subsequent nights] without having another candle in front of him or planning on getting another candle, some say if he comes across another candle, he should light it with a brachah as long as the first candle is still burning (ב"י סי' תרע"ב בשם ארחות חיים, מג"א ריש סי' תרע"ו ). It seems they hold that on Chanukah, one may make a brachah on fulfilling the mehadrin aspect of the mitzvah even if he already fulfilled the basic mitzvah. This is because Chazal instituted the Yom Tov of Chanukah with the intent that a brachah may be made on the mehadrin aspect alone, apart from the basic mitzvah (שפ"א שבת כ"א: ).
4. However, many poskim hold that in this case one should not make a brachah on the additional candle since he already fulfilled the basic mitzvah with one candle (פמ"ג א"א ריש סי' תרע"ו, ח"א כלל קנ"ד סכ"ט ).
5. Planned on lighting two. If one made the brachah planning on lighting two candles but forgot to light the second one, or he did not yet have a second candle but knew he would soon get one, all poskim agree he should not make a brachah on the second candle since he had it in mind from the start (ב"י בשם ארחות חיים הובא במ"ב סי' תרע"ב סק"ו ).
6. Two candles on the third night. If one mistakenly lit only two candles on the third night and then got a third one, or if one made an interruption by speaking after lighting the second candle, some hold he should make a brachah on the third candle. Since he already lit two candles, he showed he wants to fulfill the mehadrin mitzvah and is not relying on fulfilling the basic mitzvah. Since he has not yet fulfilled the mehadrin mitzvah – lighting two candles on the third night actually detracts from the mehadrin mitzvah – he should make a brachah on the additional candle (פמ"ג בראש יוסף שבת כ"ג ע"פ שו"ת מנח"י ח"ד סי' קט"ו, שו"ת כת"ס או"ח סי' קל"ה ).
Mistake in Kriyas HaTorah
7. If a minyan mistakenly read the parshah of the third nasi on the second day [for example], they are still yotzei since the exact day is not essential (מ"ב סי' תרפ"ד סק"ג ). If the oleh did not yet make the brachah after the aliyah, they should go back and read the proper parshah (פסקי תשובות אות ב' ). If he already made the brachah, they should not go back, even if the sefer Torah is still on the bimah. They do not need to read the parshah they missed the next day. Some say if the sefer Torah is still on the bimah, they should read the proper parshah without the brachos before and after (כף החיים סק"ח ).