When Obi-Wan is speaking with Leia on the landing platform on Alderaan, there is another ship on a nearby platform in the background that repeatedly disappears and reappears between shots.
When Owen tells Beru that Reva is coming for Luke, she gets out weapons and reasons that Reva will come when the suns go down so they should "get into position now." Hours later, when the suns are going down, they are not in a defensive position, instead they are escorting Luke into a locked room.
Obi-Wan is able to sense that Luke is in danger, and see the boy's immediate surroundings, from another planet, yet when he returns to Tatooine, he is unable to sense Luke's location and offers to join a search party with Owen and Beru to search for him. However, it's not like there were any street signs or landmarks where Luke was. It was just an exterior scene on Tatooine. It would be logical for Obi-Wan to go straight to see Owen and Beru first, to assess the situation.
Vader orders the Star Destroyer to change course to pursue Obi-Wan in the drop ship, then says he will take his personal ship down to the planet and face Kenobi himself. If he had a personal ship, he could have deployed that earlier and kept the Star Destroyer pursuing the escaping Rebels. There would have been no need to abandon the pursuit of the Rebels.