If I'm running a complex macro on a large file that I expect to take a few minutes, is it OK to do other stuff on the system (e.g. opening another application, typing in a different text editor, etc?) or could my mouse movements and keyboard inputs cause the macro to go nuts?
Indeed it is pretty safe to manipulate other programs while a macro is executed.
A macro simulates keystrokes within Vim which has no interaction with external GUI applications.
As macros don't depend on the movement of the mouse, no conflicts can appear (Or at least I've never experienced them or heard of someone who has).
EDIT As Sato observed in the comments, one element is shared between Vim and other applications: the clipboard. That means that if your Vim macro uses the system clipboard and you copy something new while it is executed, you might have unexpected results.
The best solution to this problem is to put the content of your system clipboard into a Vim register before recording the macro and to use this register in the macro.