In Chapter Twelve of Prisoner of Azkaban we find the following passage:
They turned into the corridor to Gryffindor Tower and saw Neville Longbottom, pleading with Sir Cadogan, who seemed to be refusing him entrance.
"I wrote them down!" Neville was saying tearfully. "But I must've dropped them somewhere!"
"A likely tale!" roared Sir Cadogan. Then, spotting Harry and Ron: "Good even, my fine young yeomen! Come clap this loon in irons. He is trying to force entry to the chambers within!"
"Oh, shut up," said Ron as he and Harry drew level with Neville.
"I've lost the passwords!" Neville told them miserably. "I made him tell me what passwords he was going to use this week, because he keeps changing them, and now I don't know what I've done with them!"
This situation seems a bit strange. Sir Cadogan is refusing to allow Neville into the common room – even though Neville is a Gryffindor – because he doesn't have the password. And he's obviously not telling Neville the password. Yet we then immediately find out that he has previously told Neville all the passwords in advance. If he's not supposed to tell students the password even if they are from the correct house, how did he give Neville the whole list? And if he is allowed to give students the passwords then why couldn't he just tell Neville the password when he forgot it? (And what would be the point of a password in the first place?)
And even if we interpret "A likely tale!" roared Sir Cadogan. as saying that Sir Cadogan forgot that Neville was a Gryffindor but had known that when he originally gave him the passwords, it would still render the password system mostly pointless, as the portrait would simply give any Gryffindor the password.
Edit
I'm not sure why this would be a duplicate, given that the question this is supposedly a duplicate of explicitly states that it is a follow-up to this question, and the only answer there is mine and it doesn't answer this question. Essentially, what happened was that I asked a question and someone tried to answer it. That person then realized that he/she did not know enough background information to give a complete answer to this question, at which point that person asked for the background information and I supplied the information I had been working with when asking my question.