Does bedikat chametz need to be done with the lights off so the candle or flashlight shines brightly in the room or are the lights supposed to be on in addition to the candle?
Several poskim have addressed this question, and most write that there is no need to switch off the electric lighting in a room while checking with a candle or a flashlight. The reason for this is that the electric light is not the same as sunlight, and for holes and crevices the flashlight helps no less than it does in the dark. Some, however, are particular to switch off the lights, and some turn off the lights for the beginning of the bedikah, but put them on later.
See Moadim U’zemanim, Hagaddah shel Pesach, p. 3, who writes that although some Torah scholars swith off the electric lighting, gedolei Torah rule that there is no need to do this, and each should do as he is accustomed. Yesodei Yeshurun (vol. 6, p. 338) also writes that there is no need to turn off the lights, and Chazon Ovadyah (vol. 2, p. 23) writes that some are stringent to switch off the lights, but states that there is no need to do this. This is also the ruling of Or Le-Zion (vol. 3, 7:7), who brings proof to the point from Beis Yosef (in the name of Rabbeinu Yerucham, who writes that even if one checks in daylight one needs to use a candle, and only in broad sunlight is a candle made redundant). See also Kol Hatorah (vol. 61, p. 92), who quotes from Rav Pinchas Scheinberg that it is better to switch off the light, but from Rav Shlomo Zalman that there is no need to do so, as also stated in Shevus Yitzchak (chap. 4). Orchos Rabbeinu (vol. 2, Pesach 6) also writes that there is no need to switch off the lights, and it is quoted that the custom of the Chazon Ish was not to swith off the lights (Kol Hatorah, ibid.).