I haven't been to Disneyworld during Mardi Gras before, but I will also be there on the 28th, and have done a bit of homework, so you may take this with a grain of salt. I have heard that the parks will actually be more crowded the week of President's Day (U.S.). President's Day is this coming Monday (Feb. 20th). I understand that the worst crowds will be this coming weekend, with perhaps some overflow the weekend of the 25th-26th. Hopefully, the worst of it will have died down by Monday, the 27th. However, it is technically peak season while we are there, so it will probably still be a bit crowded, although nothing like the summer months.
However, I would steer clear of Pleasure Island at night while we are there. They have a Mardi Gras celebration there that I believe lasts several days. However, Pleasure Island is not accessible with Park Tickets, and I believe the participants will be mostly Disney Cast Members and Orlando residents. My wife and I will make sure to venture into Downtown Disney only during daylight hours this trip.
By the way, Mardi Gras is the last day before Lent begins, Lent being the 40 days that proceed Easter. Catholics and some Protestants keep Lent holy by being extra pure and giving up something that is important to them during that time. Mardi Gras came about by those people who wanted to get all the debauchery out of their system so that they could be holy for Lent. I doubt there are many Americans who actually celebrate it with much more than going out to a local bar, the action having been mostly confined to New Orleans in the past, as you observed.