Physical function is what you can easily check in a device programmer. You're not using it as a programmer in this case (to permanently put data on the device), but rather a tester. For RAMs, the device programmer will write patterns into the device (which will of course be lost when power is removed) and then read them back to see if the readback matches what was written. It then repeats with several other patterns specifically designed to expose problems. If everything compares "right", then the device is good.
ROMs can be tested in a similar manner by reading them and comparing with what is known to supposed to be on the device. A good tester will also test over varying Vcc.
There's no way to verify functionality via physical (visual, mechanical measurement, etc.) inspection. What you could do if there's more than one identical chip (not familiar with the F3 hardware) is swap the RAMs around. If the problem manifests itself differently, then a RAM is bad. If the problem stays 100% the same, then it's probably not the chips you swapped (though part groups that make up a wider data bus than a single part can sometimes produce similar results when swapped around - pay attention to all details). Of course, having a known-good spare is even better: swap that in for each candidate "bad" part, and see what happens. If the problem goes away, you've found the bad part (and fixed the problem). If the problem remains, look elsewhere (or suspect multiple bad devices).
There are generally several things that can cause bad sprites ranging from bad ROMs to bad RAMs to improper address decoding to simply corroded traces (resulting in poor/broken connectivity). ROMs and RAMs are usually the easiest to test without a logic analyzer and/or detailed information on how the system is otherwise built.