We of course can't give you a definitive analysis of the condition of your new finish based on a few pics. But here's a little background. Most pebble finishes are installed with a two-step process. They blow in the pebble finish and trowel it into place on day one. Then on day two they come back and acid wash the new finish. This acid wash burns away the plaster that is hiding the little pebbles. With just the right application (and subsequent neutralizing) of the acid, the amount of plaster that is removed is just enough to reveal the pebbles, but still leaves enough plaster to hold the pebbles in place. You can imagine how easy it would be, for someone that doesn't have the required amount of experience or skill, to remove too little or too much plaster.
Your pictures look to me to indicate that too much plaster was removed. In one pic, it looks a lot like you've got some missing pebbles, even missing clusters of pebbles. In another pic, it looks like all the pebbles are missing, and only plaster is left, with dimples showing where the pebbles were. Is that what you're seeing? And how deep have you looked? I had a similar disaster in my pool and the deep end was 10 times as bad as what I first saw in the shallow end.
The contractor's promise that this can be mitigated by patching and sanding is, at best, not ideal, and at worst an outright fraud. Sanding some of these areas would not restore the missing plaster, let alone the missing pebbles. I suppose patching could work, if that's possible. But will it match? Will it adhere? And for how long? There is no question that needing to patch and sand a brand new pebble finish is not standard, and I would say "sub-standard." Which means that alone is evidence there were at least SOME installation problems.
If this theory of missing plaster is correct, there is a bigger concern. Even if the contractor can somehow cosmetically repair the areas that have lost their pebbles, what's to be done about some amount (or all?) of the rest of the surface where the strength of the bond between the plaster and the pebbles may have been compromised, but has yet to reveal itself?!?
What you need to guard against is that they will perform this patching to hide what I think is a bad installation, maybe even multiple times in the coming years, to get them past their warranty period. And then when things really come apart after that, or you eventually realize that your pebble finish has deteriorated a decade before its time, you'll be out of warranty with no recourse. Now is the time to deal with this, even before the contractor does.
So... the first step, BEFORE the contractor is allowed to make any patching or sanding corrections, is to call in PebbleTec for a warranty evaluation. Or if you want to maintain a good relationship with the contractor, do him the courtesy of asking him to contact PebbleTec. If he refuses, or balks, then you make the call. If your contractors is a certified PebbleTec installer, your new finish should be backed by PebbleTec's warranty. They have been known to send out their own rep's to evaluate an installation. This needs to happen BEFORE the contractor can disguise his work. PebbleTec needs to see the problem, first hand. A meeting between you, your witness (important!), the contractor and PebbleTec needs to occur to ascertain best next steps, before any next steps are taken. Don't settle for less.
If that doesn't work, then we can talk about other recourses. In the meantime, try to have a person with you, ideally not a relative or spouse, for any meetings with the PB, the pebble installer or PebbleTec. You might need a witness at some point. This could very likely resolve itself as the installer and/or PebbleTec should do the right thing. But you don't want to be left hanging if they choose to act otherwise. After each meeting or phone call, follow up to all attendees with an email that accurately and dispassionately summarizes what was said. Just the facts. This accomplishes two things. It establishes a paper trail of events. And it sends a very clear message to all involved: that you mean business and are taking appropriate steps to protect your investment.
If you have not made all your payments for the construction, you can safely not make any more. Keep yourself some leverage. CA has provisions for this move. Don't push the how's and why's of executing such a step just yet, not until someone demands payment. Then I can better explain that part of the process. Hint: you are embarking on what is known as a "good faith dispute," but you don't want to fan those flames just yet. The best solution for now is for all parties involved to work cooperatively, without their hackles up.