You use the beginning of this quote in your question:
Harry saw something that distracted him completely , the silhouette of an enormous shaggy black dog, clearly imprinted against the sky, motionless in the topmost, empty row of seats.
Harry's numb hands slipped on the broom handle and his Nimbus dropped a few feet. Shaking his sodden bangs out of his eyes, he squinted back into the stands. The dog had vanished.
In this case, Sirius came only to see Harry fly, just for a second. Everyone was focused on the game, it was raining pretty nastily and vision was impaired for everybody, and he was there only for a second. Then he went back to the forest:
"I've been living in the forest ever since, except when I came to watch the Quidditch, of course. You fly as well as your father did, Harry...."
So Sirius was living on the grounds in the forest as a dog, like Crookshanks. On one day he took a risk to see Harry fly, but nobody saw him because of the reasons I already laid out.
The next two instances you speak of are trivial. The first one can be easily dismissed. It was night and only Ron was with Harry at the time. Harry stops and lights his wand so they can see, but it's only Crookshanks. It probably was Sirius in this case, but only for a moment, and nobody else could have seen.
The other one is even easier to dismiss. He sees the Grim outside the Gryffindor window. It's all dark, as Ron says when Harry has to wake him up because it's like 5 in the morning. There's no way anyone else could have seen him, let alone Snape or Lupin.
The fourth time, when Sirius pulls Ron into the Whomping Willow, Lupin does see him on the map.
"And then I saw another dot, moving fast toward you, labeled Sirius Black.... I saw him collide with you; I watched as he pulled two of you into the Whomping Willow --"
And Snape did too:
"Lying on your desk was a certain map. One glance at it told me all I needed to know. I saw you running along this passageway and out of sight."
The only question remaining is that of how Lupin didn't see Sirius during the second half of the year when he had the map. There are two answers I can think of. One is that he didn't really look at it until that night. Possible, but I don't think so. In this year, with the threat of Sirius and stuff, it's likely he would look at it. If he did, he probably just didn't look in the forest, where Sirius was. It was probably swamped with dots of animals [citation: Harry sees Mrs. Norris on the map in chapter 10 of PoA] and he just didn't look there, or if he did, didn't see Sirius. As to why he didn't see Pettigrew, that's a different questiondifferent question