tdg:
would I have to change any of the code to work with the Mega?
It depends on the code. As Wawa said, if your code is just reading analog inputs, there will be no changes needed.
Some of the pins on the Mega do have different properties. For example, if you're using the SoftwareSerial library, some of the pins that you can use on the Uno can't be used on the Mega. Of course, the Mega has extra hardware serial ports, so it's unlikely you would even bother to use the SoftwareSerial library on that board.
There are some differences between the boards when writing low level code, but the Mega has been around so long that pretty much any library that has such low level code for Uno will have been adapted to support the Mega as well. You might find some sketches online that have low level coded written only for the ATmega328P of the Uno, but it will be pretty rare.
tdg:
Is there anything else that I should consider before switching over to the Mega?
The board is larger than the Uno, which might be a concern for specific projects if size is a factor.
The board is more expensive than the Uno. This means a "magic smoke" incident is a bit more expensive. For this reason, I normally recommend that beginners start with an Uno or Nano. That way they can feel more free to experiment without being so afraid of ruining their board. However, when you need the extra resources of the Mega, which it sounds like you do, then it's worth spending that little bit extra. For my own daily experimentation, I actually do use the Mega because the extra memory means I don't have much worry about running out of memory. But for a finished project, I always use a cheaper/smaller board unless I really need the extra memory or pins of the Mega.
tdg:
I assume the online Arduino Editor would interface with the Mega in exactly the same way as the Uno, correct?
Correct. You only need to select the Mega from the boards menu, just as you would for the Uno.
