I've been selecting the .bin files for multi-track and multi-CD games. I guess I'll be selecting the .cue files instead from now on, but would this have caused me to experience any problems down the line?
To swap CDs, support was added early on: inside the game, return to the main menu (press Select+Start), and you'll see 'Swap CD' menu entry. As Dmitry mentioned, you just select the new .CUE/.BIN and the game that's running will get sent an emulated 'lid-open/lid-closed' interrupt sequence and can thus tell that a new CD is inserted.
Only time you really need a .CUE file is if the game has multiple .BIN CDDA audio tracks. Otherwise, selecting the .CUE is the same as selecting the .BIN.
In the future, if you want to make your life *really* easy, and can find your game packaged as one, use PSP Eboot files (.PBP extension).. they offer multiple advantages: compression, multi-CD packaged in one file, no CUE worries. You'll still need to swap CDs when the game asks for a different disc, but the 'Swap CD' menu will simply contain 'Disc 1, Disc 2, etc' rather then making you navigate a dir to choose a file manually.