I understand from this answer why not-so-bright Harry didn't understand the true usefulness or significance of the two-way mirror until it was too late. This was basically because Sirius described it to him as an emergency method of contacting him if and only if Snape was giving him a hard time.
"What is it?" Harry asked.
"A way of letting me know if Snape's giving you a hard time. No, don't open it in here!" said Sirius, with a wary look at Mrs Weasley, who was trying to persuade the twins to wear hand-knitted mittens. "I doubt Molly would approve - but I want you to use it if you need me, all right?"
"OK," said Harry, stowing the package away in the inside pocket of his jacket, but he knew he would never use whatever it was. It would not be he, Harry, who lured Sirius from his place of safety, no matter how foully Snape treated him in their forthcoming Occlumency classes.
(Order of the Pheonix, Chapter 24, Occlumency)
Here we can see that Harry is worried about Sirius' increasing recklessness. But he also doesn't understand that the mirror will work as a general communication device. So when he wants to contact Sirius for other reasons - to talk about the Pensieve and to enquire as to Sirius' whereabouts - later in the book he thinks that the only way to talk to Sirius is to use Umbridge's fireplace.
Harry thinks this but Sirius knows better. Why didn't Sirius ask Harry why he wasn't using the mirror that Sirius had given him for the exact purpose of getting in touch? Surely he should have been bewildered as to why Harry was using the much more risky method of Floo powder? Is there a good reason why Sirius didn't effectively say, "Let's continue this conversation using the mirrors?". Obviously hindsight is a wonderful thing but it would have saved a lot of trouble later on.