When shopping, some children are afraid of using the big potty. It's loud in there, the toilet is large, the flusher is loud - who can blame him? You can help by bringing along a seat that fits in the regular toilet. This can be large and cumbersome, but since the diaper bag isn't full of a lot of diaper paraphernalia any more, chances are you can find a seat that will work. If you're not up for that, then try kneeling beside your child while they are sitting and hold their hand or their body if they seem scared about slipping in. Another thing to try -- sit as far back on the toilet yourself and then put your child in front of you.
You never know when potty emergencies while shopping may actually work to your advantage. My son was withholding his bowel movements for days and days at a time and did not ever want to go in a public restroom. One day, when I knew he'd been holding it for some time, we went to a toy store. I figured this was somewhere he enjoyed a lot so he would be relaxed. We walked around that store for hours until the urge struck. He asked me for a diaper and I told him I didn't have any and that he'd have to go in the toilet if he really needed to go. He wanted to get back to looking at toys, so sure enough -- he used the toilet there at the toy store and it set a precedent for pooping on the potty.
Visiting Friends or family
When visiting friends, you've got a little more flexibility. You can bring a potty chair along, as well as any dolls and books your child might enjoy while going to the bathroom. Just make sure you outfit your child with plastic pants or perhaps even use pull-ups if you have a friend who is uncomfortable with accidents on new furniture or floors. Make sure, too, to explain how you handle accidents and make sure that others are going to maintain a positive atmosphere for your child. Ask about any special bathroom issues, for example -- is the toilet very loud, is the toilet paper hard to reach from the toilet, is the light easily accessible or does the toilet have any problems flushing?
There are some great potty chairs available today for road trips. There's an inflatable potty (Inflate-a-Potty) that uses regular trash bags for liners. You can pull over and go right there if you're not close to a gas station or rest stop. These chairs are inexpensive enough to equip every vehicle you own. Make sure you've got changes of clothing and wipes around just in case, of course.
Concerts, fairs and other events
The inflatable potty will certainly work for these situations, and there's another chair that folds up like a suitcase that your child can carry himself, if you're already carrying a load of stuff around. I'm not sure the chair always works as intended, however. I have a friend who has one of these, and wanted her daughter to carry it around at a craft fair because she knew she'd be buying lots of items. Her daughter would not use a public potty if it were the last toileting option available on the planet. Well, after lugging it around all day that day, she decided that she'd use the public potty at the next craft fair.
Potty training on the go is a little bit like being a Boy Scout. No matter what your method, you've got to "be prepared." Try to get your child to use the bathroom before setting out on your trip, and make sure you've got everything you could possibly need before heading out the door. More clothes are better than fewer, and remember that the moment you decide the wipes are just too much of a hassle to bring, your child will break out with the worst case of diarrhea you've ever encountered. Most important of all, though, don't forget to exercise the same patience while out with your child that you do when potty training at home.