Alarm clock mixes

Short answer is yes and yes.
 
A good grot box (Avantone or similar box) can reveal deficiencies in a mix especially in the midrange and a good way to check levels of tracks (balance) i.e vocals ,bass etc..This is also why many people love yamaha ns-10's (matter of personal taste, of course). I would vote for a good grot box though (don't need a pair, just one grot box, and remember mono is your friend when it comes to final mix checks).

It's important to be in the habit of listening in different formats and contexts.

I've got things set up so I'm just a button press away from choosing between my monitors, some fairly nice hi-fi speakers, a pair of pretty nasty Dell computer speakers, and a headphone out with earbuds. And I've got Panipulator in the master bus of my standard template. The monitors are for doing the actual work, and the other options are for various verifications and checks.
 
I also routinely upload works in progress to soundcloud so I can listen to them on headphones while I'm walking down the street. That's a great test. For one thing, soundcloud streaming quality is pretty terrible; I think 128k mp3, more or less. And listening to 128k on earbuds walking down a busy street; well, you've got yourself a mainstream use case right there. If your mix holds up in that situation, then YOU DA MAN.

What is the industry standard for Pan Law and mono mixes?  I notice the Panipulator has L+R 0db, -3db, and -6db as options...and despite reading about this I'm still confused.
 
What kind of mono is my clock radio playing??? 

There's no standard as such. Different mixing consoles have historically had different pan behaviours. The various pan law settings let you get an approximation of something you might be used to.
 
Broadly speaking, a centre dip will make volume seem more consistent across the full width. That's all it's for, really.