The Shulhan Aruch (Orah Haim 453:4) says that it is proper for theMatza that is used for the different Mitzvot during the Seder (ie. Achilat Matza, Korech, Afikoman) be made from wheat which was closely watched over from the time of its reaping (“Matza Shmura”). During the rest of the holiday, however, one does not need to eat Matza Shmura.
Another is issue is the propriety of eating machine-made Matza. Some rabbis, mainly Ashkenazic, were concerned that during the grinding of the wheat kernels, moisture would be pressed out and would lead to inadvertent leavening of the dough. Indeed, Rabbi Raphael Benaim (Sefer Kol Tehina-Kol Tehina) as well as several Algerian rabbis forbade eating machine-made Matza on Pesah for this reason. Nowadays, the machines used to produce Matza are more refined than what existed previously and this concern no longer exists. Nevertheless, one issue with machine-made Matza is that there is a possibility that they are not made for the sake of the Mitzvah of Matza. Rabbi Ben Zion Abba Shaul (Or LeZion, vol. 3, ch. 11, Q. 7) says that the Matza used for the Mitzvot of the Seder should be hand-made. For the rest of the holiday, he says that the Matza which has a more reliable kosher certification should be used since it is more likely that it was produced for the sake of the Mitzvah of Matza. It should be noted that during the Shulchan Orech section, which is the actual meal, one may consume machine-made Matza.
Summary: Hand-made Matza should be used for the different Mitzvot at the Seder (Achilat Matza, Korech, Afikoman). Machine-made Matza may be used for the actual meal and for the rest of Pesah so long as they have a reliable Hechsher.