"He is as clumsy as he is stupid."
Is he, though? We're told Admiral Ozzel is stupid, but upon careful reflection, I've concluded this is not actually the case. Consider the following:
1. The scene where Ozzel demands "proof, not leads" is meant to show his lack of initiative (even though this will be contradicted later). But he's completely right. All the image of the power generator was proof of was that it was a settlement. But he's portrayed as idiotic and unimaginative for so much as suggesting it could be anything other than the Rebel base. Note Ozzel never says they shouldn't go, just that the odds are against it being the Rebel base; the most he seems to want in that scene, from Vader or Piett, is a little more evidence before they throw the entire fleet at some random podunk ice planet based on what amounts to nothing. If it hadn't been the Rebel base, Vader would've really had egg on his face. Piett, in contrast, is meant to be seen as imaginative when he's really just making a deductive leap that their boss just happens to agree with for some reason. But it is the only time Piett will be portrayed as creative or useful.
2. In a direct contradiction of the earlier scene portraying Ozzel as lacking initiative, he's full of it (initiative, that is) when he orders the fleet out of lightspeed so close to the planet in what he hopes will be a surprise attack. The cautious Ozzel in the earlier scene wouldn't have done this; rather, it's something Piett, as previously established, would do. But for some reason they've swapped roles; Ozzel has gone from cautious to reckless, and Piett has gone from being a go-getter to just going along with his superior, and he'll never recover from this reversal (more on this below).
3. Did Ozzel's decision to bring the fleet out so close to Hoth actually affect anything? Yes, the Rebels had time to put up the shield, but wouldn't they have done that no matter what? If they came out outside of the system and then approached (which seemed to have been what Vader wanted), the Rebels would've had even more time to prepare; they certainly would've been able to do more than just put the shield up. Like prepare a proper defense or evacuate way more ships. But because the fleet sprang on them like it did, even with their foreknowledge that the Imperials were coming thanks to the probe droid, they had to scramble and rush everything, and lost poorly as a consequence. Ozzel's surprise attack worked! Unless Vader really did intend to bombard it from orbit (and Veers' emphasis on the shield's effectiveness against that suggests he did), then a ground invasion taking the base by force was going to happen no matter what.
4. And if not a ground invasion, then what was Vader's idea? If he wanted to bombard the base, wouldn't that risk killing Luke, the guy he wants alive and not a pile of ashes?
In summary, Ozzel is portrayed as an idiot for insisting on something silly like evidence before putting all the Imperial fleet's eggs in one basket, he and Piett switched characterizations between scenes and then he was killed for a surprise attack that actually worked, and Vader somehow simultaneously wanted to destroy the Rebel base from orbit but also capture Luke alive, meaning our dear Dark Lord effectively held two contradictory thoughts in his head at this time.
What would've made way more sense is if the opposite happened; Ozzel remained the cautious man he was in his first scene and held back from rushing in, giving the Rebels time to prepare adequate defenses, and then Vader gets mad and kills him.
Now, as for Piett, we're asked to see him as being more competent than Ozzel, but I see no evidence of this. Outside of his introductory scene, he is never anything but a yes-man to Vader. He does not speak his mind or display any initiative throughout the remainder of his appearances. He just does what he's told, incapable of standing up to Vader the way Ozzel does in their first scene. He tries, during the asteroid scene, but doesn't even manage to finish his sentence before Vader interrupts him, demands they continue on their clearly suicidal course, and the mousy little man knuckles under and never again dares to actually be a commander. He fails at the one task he's actually given (ensuring the Falcon stays disabled), and then in his second movie, he just blindly follows the stupidest order ever and lets himself be hamstrung by Palpatine's addiction to being showy, rendering the Imperial fleet basically useless by turning them into just a blockade that wouldn't have worked even if escaping had been the Rebels' plan, considering it's, y'know, space, and lining your big ships up in a row isn't going to do much when they can fly over you, under you, or go in literally any other direction than towards you; they don't even encircle the Rebels, they just line themselves up and sit there. And the worst part is, Piett doesn't act like he thinks this is the worst idea ever; when Gherant protests, Piett stands a little straighter and says he has his orders from the Emperor himself. He's too proud that Papa Palpatine spoke to him personally to bother with whether or not turning your fleet into a glorified roadblock that won't even work is a good idea. Even when the Rebels started actively targeting the sitting-duck Star Destroyers, Piett refused to disobey Palpatine, even to save his own life. If he'd had the Star Destroyers go on the offensive instead of simply sitting there defending themselves, he might've won the day (and then probably been demoted or worse for disobeying orders).
So, ignoring the first scene aboard the Executor where Ozzel emphasizes caution and Piett shows initiative, I think that what Vader wants out of commanders aren't people that are good at their job; he wants yes-men who'll tell him what he wants to hear. Even Jerjerrod is not allowed to make his perfectly reasonable point that he can't do what Vader is asking without more men and more time, because apparently nobody ever told Vader that rush jobs inevitably end up sucking.
But I guess that's the Empire for you; they want it done yesterday, regardless of whether it's possible with the time and materials provided, and to heck if it works or not, and if it doesn't, then it's your fault and not theirs.