I have some cuttings I moved up into clear 32 oz deli cups. Drilled lots of holes, gave them some food and overall they're doing great. I noticed the ones I am putting outside during the day - my graduates who do not go into the humidity bin - have some white mold on the inside of the cups along where the soil hits the cups. 

I think I know why - I gave them some water and while the top is open, they are still in a bin to make it easier for me to move them around the yard. Moisture plus not much air circulating between the various cups lead to my issue. So beyond removing them from the bin and moving them around the hard way, anything else? I'd hate to repot them and start over with fresh material but if I have to I will.

Would it be possible to transport them in the container and then set them outside it while they sunbathe, put them back in for the return trip? I wonder if the baking soda or peroxide idea would work on the mold on the cup the way it does on the cutting?

That's what I plan on doing. Before I was letting them stay in the container which ended up being a bad idea.
I recalled the peroxide trick with cuttings but wasn't sure if it applied in this type of situation?

I don't think it would hurt to try before yanking everything and redoing it all.

The mold won't go away unless you you exterminate it first.  After that, what I like to do to my cups is to squeeze them gently once in a while to promote air circulation.  I have read here lately about hydrogen perodixe and has adopted it.  It does get rid of the mold instantly.  But like I say, you need to have preventive practices to prevent mold coming back.

in theory, mold should spread and will infect other cuttings near by. the spores are easily disturbed and what not. but funny thing i have noticed is, the mold are localized and will not move to other cuttings. maybe it's because i catch them fast enough with daily check.

anyway.. if it's inside of the cup, water it with diluted hydrogen peroxide. or uppot to 1 gal and while doing it, get rid of the part of the soil that has the mold.

i had mold inside of one of the cups. since i use peat pot method, i just took it out, clean out the side of the peat pot with mold, spray H2O2, and repot. it never came back. but now i make sure i have holes on the side of the cup for whatever little circulation it requires.

Nichole,
I've had that same problem but, with mold on top of the soil of my kiwi cutting's.
I used 1 table spoon Neem oil in a quart of warm water, with a teaspoon of dish soap.
Shake well before using, Works instantly! usually only one treatment needed.

Are you sure that they are mold? Those white moldy spots, could be either the fine feeder roots or very small roots. If your plants are growing fine, leave them be. Just monitor them closely.

Good luck,
Navid.