OPINIONS: It is a widespread custom to roast a shank bone the day before Pesach and place it on the Seder plate to commemorate the Korban Pesach (Shulchan Aruch OC 473).
The Mishnah earlier (53a) states that there are places where the practice is not to eat roasted meat on Pesach night in order not to appear as though one is eating Kodshim ba'Chutz, sanctified meat outside of the Beis ha'Mikdash. The TUR (OC 476) and other Poskim write that in their areas, it is the custom not to eat roasted meat on Pesach night.
May one eat the roasted shank bone at the Pesach Seder?
(a) The Gemara here says that the prohibition against eating roasted meat applies only to meat that was roasted "Mekulas" -- the entire lamb or goat was roasted whole. If even one limb was cut off of the animal before it was roasted, the prohibition does not apply because it does not resemble the Korban Pesach.
Rashi explains that the prohibition applies only in a place that has the custom not to eat roasted meat on Pesach night. Accordingly, in all places one should be permitted to eat the roasted shank bone, which was roasted by itself, on Pesach night.
(b) However, the RAMBAM (Hilchos Chametz u'Matzah 8:11) writes that even in places where the custom is to eat roasted meat on Pesach night, one may not eat roasted meat when the whole lamb was roasted. The Rambam understands that the Gemara here refers to a place where the custom is to eat roasted meat on Pesach night. In a place in which the custom is not to eat roasted meat, one is forbidden to eat even a piece of meat that was roasted by itself, such as the shank bone. This is also the opinion of the ROSH (4:6).
HALACHAH: The opinion of the Rambam is cited as the Halachah by the TUR and SHULCHAN ARUCH (OC 476). The Tur adds, based on the Yerushalmi, that even the meat of a calf or fowl, or any animal that requires Shechitah, may not be eaten roasted on Seder night. Roasted or fried fish is permitted, because fish does not require Shechitah.
Does the prohibition apply to Pesach morning as well? The CHASDEI DAVID (on the Tosefta quoted in the Gemara) asserts that the prohibition applies in the morning as well. However, the DARCHEI MOSHE (OC 473) writes that the prohibition applies only on the first night of Pesach, as the Tosefta itself implies ("Leilei Pesachim").
The Tur also mentions that it is a "proper custom" ("Minhag Kosher") to eat cooked meat during the Seder. It is not clear exactly why he calls it a proper custom. The TAZ suggests that it is proper because of the obligation to experience Simchas Yom Tov through eating meat, while at the same time avoiding meat that was roasted. (Cooked meat might also serve to commemorate the Korban Pesach, even though the Korban Pesach was roasted.)