Outside of the dumb hacking scene and the flaccid play at Moore-esque hijinks with the CGI Komodo dragon, Skyfall is a very good Bond film. If you're a fan of the series the elements that stretch belief are pretty part and parcel with a lot of the movies, many of which have plots that are so poorly delivered to the viewer that it's almost impossible to actually understand what is happening and why (I dare you to tell me what the plot of Octopussy is. Even The Living Daylights, an otherwise pretty great movie, is incredibly hard to decipher). But that's part of the charm of the movies imo. Casino Royale is on another level, but it's on another level compared to pretty much the whole series, so I don't hold that against Craig's run which on the whole has lived up to the standards of the series. I would have like another movie or two that kept the same tone as CR and QoS though before leaping back into stylization and nostalgia.
I'll always hate the part where he lets Berenice Marlohe's character die, too. So cruel in such an un-Bond way.
It depends on the interpretation of Bond. It's very much in line with how Bond is depicted in the Casino Royale novel, where he coldly rationalizes Vesper's hypothetical death as a consequence of him trying to get Le Chiffre, and blaming her for it for being stupid enough to get captured.
But I think he didn't attempt to save her not because he was being super cold but because he underestimated Silva's ruthlessness. It's a very Bondian scene to have him engage in a "gentleman's" gambit with the villain only to have the villain cheat. I don't think he expected Silva would just shoot her in cold blood and he was buying time (thought the scene would work a lot better if his gun-fu skills immediately after she's been shot were more sloppy to better explain why he didn't try it while she was alive)