Are there significant differences between the Rambam Haggadah and the current mainstream Haggadot that are in use?
Some highlights (you can glean this by simply reading Mishna Torah, but of course you have to compare it to a regular seder):
- Say a Bracha Achrona on the wine after every cup (at least according to this)
- Say a Bracha when washing before Karpas. Latter day practice has been to not say a bracha in deference to Tosfos opinion.
- Dip the Karpas in Charoses, not saltwater. The Rambam holds Karpas has a Chiyuv to be eaten, and all things to be eaten require dipping in Charoses.
- Eat a Kezayas (at least) of the Karpas. Many specifically eat less than a Kezayas of Karpas (following the Haagaos Maimonis on the Rambam).
- Specifically a kind of meat to represent the Korban Chagigah, not an egg (it isn't necessarily obvious he would disqualify an egg, though).
- The seder leader, not the children, asks the Mah Nishtanah. (This is debated if it is his intent or not, see the אדני יד החזקה to Chametz Umatza 8:2). The children or their substitutes still need to ask, but perhaps not the Mah Nishtana as we say it, just the general 'why is it different'.
- The order of the questions is different, in that it starts with the dipping (not unique, but certainly unusual, at least by Ashkenazi standards).
- The implication is that the Matzah isn't necessarily in front and shown while saying most of Maggid (the table is taken away).
- The Rambam himself describes moving the table back and forth, which is out of style due to our large tables. It is a matter of speculation what he would say to do where people don't really have small tables any more.
- There is no Dayainu, or the whole section about how many miracles were at the sea.
- He only calls for two Matzahs, one broken and one whole (that isn't unique, but it is more uncommon) instead of three.
- He calls for dipping the Matzah in the Charoses (as above, all Mitzva-eating requires Charoses).
- He allows for eating roasted meat at night, if that is the local custom. Yemenite apparently do have that custom. That isn't different halachicly, really, it is just that the mainstream custom is to not.
- Hallel for the fourth cup ends at the regular Hallel. He has an optional fifth cup for the Hallel HaGadol (Tehillim 136). Generally the Haggados include the Hallel HaGadol in the fourth cup. The Rambam has been generally understood to mean that you drink this fifth cup. The Lubavitcher Rebbe (Likkutei Sichos Vol. 27 p. 48ff) argues that he only means that you poor it, not drink it.
- There is no Kos Shel Eliyahu ceremony, although the Vilna Gaon is quoted in Ta'amei HaMinhagim as arguing that Kos Shel Eliyahu is poured and not drunk in recognition of the argument between the Rambam and others that there should be a fifth cup. Regardless the Rambam has something different said over that fifth cup and puts it as a fifth cup to be poured after the fourth is drunk, which is different than how other Haggados have it.
I left out most textual difference in the Haggada proper, and this list is not intended to be comprehensive, especially given the ambiguity in the term "mainstream".