A class asked about the meaning of the roasted egg on the seder plate. It's a good question, because the egg just sits there. We don't eat it; except for stating that it's required on the seder plate, the haggadah never refers to it.
In contrast, we eat the karpas, the charoset, and the maror, and the haggadah text refers explicitly to the zeroa, the shankbone. So what's the purpose of the egg?
A student in the class suggested that the egg symbolizes new life. This is the explanation that I learned as a child, and it makes some sense, because the exodus from Egypt marks the beginning of the life of the Jewish people as a nation that will eventually settle in the Land of Israel.
On the other hand, it's not obvious that "new life" needs to be symbolized on the seder plate at all, and the absence of any reference to it in the haggadah text still requires explanation. It's a bit like saying that the karpas symbolizes spring: since Pesach always falls in the spring, a specific symbol of spring is not really as important as it might otherwise be.
Also, it fails to explain why the egg is roasted. Logically, an egg symbolizing new life might have to be raw and fertile.
Another explanation sometimes given is that the egg represents the sacrifices that are no longer carried out. This has the virtue of explaining why the egg is roasted, but since the zeroa represents the Pesach sacrifice, which is stated explicitly in the haggadah, it's still not clear why the egg is required.
Furthermore, at one point in the seder--korekh, the "Hillel sandwich,"--the charoset seems to represent the Pesach sacrifice! The text states, "With matzah and maror shall you eat it," and it originally referred to the sacrifice, but it's actually the charoset that we eat with the matzah and maror.
I usually answer that the haggadah was written by a committee. Like many collective works, it includes the ideas of multiple authors, even when these ideas are inconsistent or redundant.
Thus, the requirement to have a roasted egg on the seder plate may represent the opinion of one rabbi or group of rabbis, while the shankbone represents the opinion of others. Perhaps those favoring the egg also suggested an addition to the haggadah text that would have referred to it, but their suggestion wasn't adopted. Who knows?
It may also represent an established custom that the rabbis of old didn't endorse, but felt unable to abolish. Leaving the egg on the seder plate without any reference in the haggadah text would have been a compromise.
I see the first washing of hands in the seder in this way. No brachah is said then, which also requires some explanation. Conventionally, people say that there is no brachah so that people will ask why there is no brachah, which just sounds silly (unless you think that it is desirable to ask as many different questions during the seder as possible, in which case anything that is odd or inexplicable has merit).
My take on washing hands without a brachah is that the rabbis weren't certain that washing hands at that point in the seder was actually required. The idea of a brachah shel mitzvah is that one says it before performing a specific mitzvah, so if the action isn't known to be a mitzvah, or is there is doubt, usually no brachah is said. We wash with a brachah before eating the matzah, just as before eating ordinary bread, but the first washing of hands precedes eating only a very small amount of a vegetable.
But some of us have another case of a food item that we place on the seder plate, but to which the haggadah never refers: the orange. Ordinarily this is described as representing women who were excluded from full participation in Jewish ritual.
There are several midrashim about the orange currently in circulation. All attribute the origin to Susannah Heschel. Her own account of it dates to a presentation she gave a number of years ago at Oberlin College. As she describes it, someone asked her opinion of the then-new practice among Jewish lesbians of placing a piece of bread on the seder plate as a protest against their exclusion from the mainstream of Jewish life and thought.
Heschel was uncomfortable with placing something treif on the seder plate, especially if the goal was for Jewish lesbians to gain acceptance, in other words, to become kosher in Jewish society. She suggested instead placing something totally new, such as an orange, on the seder plate--something that would not, in and of itself, transgress, but which could add new meaning.
Most households that place an orange on the seder plate don't make a formal addition to the haggadah text for it. Similarly, some add a kos Miryam, a Miriam's cup (of water) to the seder table even though most haggadot make no mention of it.
To some extent, the kos Miryam seems to have displaced the orange as a feminist addition to the seder table. For those of us who worship in settings where women participate fully, and where women serve on the boards and hold office in our congregations, the need to symbolize the exclusion of women from Jewish life, the purpose of the orange, no longer seems compelling. The kos Miryam may turn out to be a more enduring addition, because it symbolizes the omission of women's roles from our texts and history.