Often coaches take a kids lack of skills as just that: lack of skill and will drill them up an down the hill with poor results... Often though, it's not as much a lack of skill as it is poor equipment. As a parent, you should also be mindful that kids grow quickly and a good boot could turn into a torture device within half a season.
Here's what I check and why - please help me by adding more things to keep an eye out fo, with your comments below.
The thing to check first is normally the DIN settings - parents are responsible for that, but if a kid comes out of his skis too much, maybe double-check the DIN and correlate with age/weight/skill. Send them to the technician if it doesn't look right.
If a kid can't turn - maybe the skis are hopelessly railed. Take their skis off and quickly check their bases - you don't need a true bar, a strait enough pole is enough to see if it needs a base grind or not. Are the skis too long or too stiff?
Are the bindings mounted properly? Do they seem to be in the proper place? What if they're too far back and he can't do much but slide the tails around?
If he's back too much and never comes forward to bend the skis, maybe the boots are obviously too stiff...? The same happens though if the boots are too soft, mind you. Have a quick check: he should be able to comfortably bend the boots but not easily. Also, the boots may be too high in the front - most newer junior boots have a lower shell in the front, to ease getting forward... you can quickly compare it with that of other kids of similar size.
If she takes forever to turn, can't keep up with a course... Did she get her third hand bots from her cousin and they're hopelessly worn and her feet floating inside? A boot does need to be tight fitting, to give any control over the ski... If the boot does fit nicely however, she possibly needs canting? Are the skis too long or too stiff?
Knock-kneed skier, too much A-framing going on? Well, first thing to check is the stance, because it's easy: if it's too wide too early in the turn, he will be A-framed and it's easy to correct, see Skiing - the wide stance debugged. But if the stance is fine, maybe the boot is not aligned properly, specifically the upper cuff. Maybe he needs canting on top of that?
Read more about Ski Boot Fitting.
... that you should want ot avoid, of course:
To be continued - in the mean time, read more Ski Coaching Ideas.