In order to fulfill a mitzva on the festival, whether it is incumbent upon an individual or a group, unskilled labor may be undertaken. A mitzva need is comparable to other festival needs for which it is permitted to do unskilled labor (Rema 544:1; MB ad loc. 8). In contrast, skilled labor is permitted only to take care of bodily needs on the festival, such as preparing food or fixing the water system (above 11:3-5).
Therefore, one may not write a Torah scroll on Ḥol Ha-mo’ed. It is prohibited to write even one letter, as scribal writing is skilled labor which is permitted only for bodily needs (SA 545:1). However, if a Torah scroll needs an unskilled repair, it may be repaired on Ḥol Ha-mo’ed. This is the case even if the Torah scroll is not needed on Ḥol Ha-mo’ed, since it is permitted to do unskilled labor on Ḥol Ha-mo’ed for a mitzva, even if it does not meet a festival need. Therefore, if a Torah scroll is discovered to have an extra letter, the letter may be erased. If letters are stuck together, they may be separated. If the ink of a couple of letters has faded, they may be re-inked (Sha’arei Teshuva ad loc. 1, citing Panim Me’irot 1:66; MB ad loc. 2; AHS ad loc. 1).
One who is studying Torah may write or type up notes if he knows that doing so will improve his concentration, since it is being done in the service of a mitzva (SA 545:9; above 11:13).
If one wishes to dedicate a Torah scroll on Ḥol Ha-mo’ed, he may not leave the writing of the final letters to Ḥol Ha-mo’ed, since this writing is skilled labor. However, a scribe may outline letters beforehand and they may be filled in by someone else on Ḥol Ha-mo’ed, as this is unskilled labor which is permitted for a mitzva need (AHS 545:5; Sdei Ḥemed, Aseifat Dinim, Ma’arekhet Ḥol Ha-mo’ed §12; Kaf Ha-ḥayim ad loc. 6).
If one is making a brit mila on the day after Yom Tov and cannot prepare all the food after Yom Tov, he may prepare food on Ḥol Ha-mo’ed. Even though normally we do not prepare on Ḥol Ha-mo’ed for the weekday, in this case it is permissible since this is a mitzva need and the labor is unskilled (SSK 67:44).