Retrieving an Item Dropped at the End of Dive
If, after a dive and on your way onto the boat, you drop something in the water, is it safe to go back in to retrieve it assuming you have dive time left and air in your tank?
It's really difficult to answer this question out of context so is “it depends.” However, one of the best ways to get into trouble is to assume something is OK because “my computer said it was all right.” Computers aren't omniscient; they simply crunch numbers. They can't think or take into account circumstances that may put you outside the parameters assumed in their decompression model.
One example is that, regardless of what decompression models predict, many authorities believe that the kind of descent that you describe — often termed a “bounce dive” — is ill-advised. The reason, they theorize, has to do with silent bubbles. Divers develop these bubbles quite frequently, though not necessarily all the time. However, it's thought that most are trapped in the fine vasculare of the lungs, where they diffuse in the normal respiratory process. One hypothesis is that a quick, deep dive soon after surfacing could compress these bubbles to a point where they might be able to pass through the lung's “bubble net,” and into arterial circulation. How valid such a concern really is, we just don't know, but it is plausible.
Still, even without the silent bubble issue, there are other potential problems. Rarely does anything dropped from the surface drop directly to the bottom, so finding a lost object often turns out to be much more difficult than you might imagine. This means it almost always takes more time than assumed, and using a tank with an almost exhausted air supply is a recipe for disaster. Of course, this all depends on the visibility and water depth, so in some cases with surface-to-bottom visibility in shallow water — with very ample remaining bottom time — a quick dive back down to the bottom might not be that big of a deal.
On the other hand, it does involve some risk, which could be substantial. As you mentioned, the value of the object in question is also an issue. While I'd never consider going back just to recover a snorkel or a knife, a camera worth several hundred dollars or more could probably make me think twice. In the final analysis, it's your call, but in most cases I'd probably come down on your side of the argument.