I am a Canadian citizen, and will be entering the US by train. I then plan on taking two flights within the US, and going back to Canada by train. This is a bit unusual, in that people usually fly to and from different countries, so I am wondering, will I be able to do this without any problems? Are there any restrictions? Do I need to do something in particular when ordering my tickets? I have a valid Canadian passport.
You'll need a form of ID, but legally once you're in the country you can take any form of transport that a US citizen can. Plane, train, bus, ferry or automobile - your citizenship will have no bearing on whether you can use it.
No problems whatsoever. Foreigners take US domestic flights quite often. Just show your passport to the TSA when passing the security lane, and even your Canadian driving license might be enough - check on the TSA site.