"Alert my Star Destroyer..." ruins the pacing and logic of the scene semantically, too.
"Bring my shuttle" means Vader is leaving, and he's leaving now. He's not going to walk to where his shuttle is, he's having it brought to him. In the SE, he walks to his shuttle, which is much less urgent.
"Alert:" Something is going to happen, but it's not happening yet. While everything else is happening in real time, the command to alert someone to do something draws our attention away from the action into the future. This would be okay if the future we were considering had some direct bearing on the action ... "Alert my Star Destroyer to prepare for bombardment," etc ... but it really doesn't. Lucas breaks into the action to ask us to consider something utterly mundane.
"... to prepare for my arrival." This implies that Executor is not, in fact, prepared for Vader's arrival. There are troops in contact and starfighters cleared hot, so by this point everyone should be "prepared" for every contingency. Approach, IFF, etc should be handled by the shuttle crew and flight ops as in RotJ, there is no need for the passenger to do it. The implication behind this line is that
a) Vader expects some kind of pomp and ceremony when he boards, or
b) Executor is an inefficient ship and has to be continually reminded to be ready for the squadron commander to embark.
Either way, the Imperials come off looking kind of dumb. If Vader expects a reception in the midst of combat, he has a grossly-inflated sense of self-importance. If he is micromanaging his shuttle and Star Destroyer crews, he has a grossly-deflated sense of their competence (or they are, in fact, quite incompetent). And in both cases, the sense of urgency is deflated.
Ah, well. Star Wars is effectively dead to me. Star Trek, too. Maybe this "Firefly" thing I hear so much about will catch on.