With apologies for not elaborating on these ideas, here is a quick sampling of Rogatchover chakiros on inyanei Pesach from the haggadah:
1) zman -- A) does the start of pesach create an issur on chameitz for eight days, or does each second of pesach create a new shem issur? (Rambam paskens that one gets malkos for buying chameitz of Pesach -- it is not a lav hanitek l'aseh because each second is a new shem issur and one cannot correct the issur which has already passed). B) shetach vs. nekudah -- is there a chiyuv matzah year-round which we can only be mekayeim on pesach, or does the zman of pesach create the chiyuv anew each year.
2) chomer/tzurah -- is the idea of biyur chameitz to nullify the tzurah of chameitz or the chomer of chameitz (machlokes R"Y and Chachamim whether sereifah is required).
3) poel/nifal/peulah -- A) achilas korbanos: there is a mitzvah in the act of eating (peulah), for the meat to be consumed (poel), and for the effect of avoiding nosar (nifal); B) mitzvas milah: there is a mitzvah in the act of cutting (peulah), in the person becoming mahul (poel), and in avoiding the smel areil (nifal) -- nafkah minah: hatafas dam bris for someone born mahul, or would a person who is moshech orlaso need another milah; C) achilas matzah/ maror -- balah matzah yatzah because although there is a requirement for ta'am matzah, the act of eating is an end in itself; swalling maror is not a mitzvah because the halacha of feeling the taste is not in the act of eating but in the effect (nifal) that must be produced.
4) peulah hanimshechet -- food cannot be consumed after afikoman because the eating is a peulah hanimshechet; the act recurrs continuously as a result of the taste that lingers.
5) issur atzmi -- is chameitz a cheftza shel issur or is it the zman of pesach that places it off limits (nafka minah: machlokes R' Shimon and other Tanaim whether chameitz she'avar alav haPesach is an issur d'orasya).
6) klal vs. ribuy pratim -- A) is the mikdash a single klal inclusive of its keilim or is each kli a seprate prat that is required to create the klal of mikdash (see Rambam/Ramban in Sefer haMitzvos whether the menorah, shulchan, etc. are counted a seperate mitzvos or are included in the general mitzvah of binyan mikdash; B) is a zimun or tzibur a quantity of pratim or a seprate new qualitative klal (this is the machlokes Tanaim in Brachos 4:5 whether the nusach of zimun changes with the addition of more people or not [i.e. if zimun is a qualitative entity, one cannot have more or less of it]).
Some other ideas that you Briskers may be familiar with:
6) gavra/cheftza -- is chameitz an issur gavra or an issur cheftza (interesting nafka minah: is a chatzi shiur chamietz created before pesach mitztaref with a chatzi shiur created on pesach; nafkah minah as well whether there is bal yer'ah on a ta'aroves chameitz -- is the ta'aroves a cheftza of chameitz or a seperate issur gavra to eat).
7) two dinim: hallel of chanukah and purim is a mitzvah derabbanan of keriah; hallel of pesach night is hallel of shirah and a chiyuv d'oraysa.
If I whet your appetite you still have a few days to get to the seforim store...