There is another thread on this topic, and the link is below.
That said, the dome car is about as uncomplicated as you can get.
Seating is on a first come, first served basis, your reserved seat on the Adirondack is your coach seat, you can come and go into the dome as you wish.
From reports of riders of past years, there is no great clamour for the dome seats, so you should have no issue in finding space.
That said, given that the dome has not run on all the days it has been supposed to, I would check with the 800 number to verify that it will be running on the date
that you wish to travel, and given that it is the last dome car Amtrak had on-hand, you never know which year will be it's last.
Remember that the Adirondack is a limited service, state supported day train, there is no checked baggage service, no business class, just a cafe car.
Ken
http://discuss.amtraktrains.com/index.php?/topic/65698-great-dome-on-the-adirondack/