From Prisoner of Azkaban, after the attack on the Fat Lady by Sirius Black:
"And the Fat Lady, sir?"
"Hiding in a map of Argyllshire on the second floor. Apparently she refused to let Black in without the password, so he attacked. She's still very distressed, but once she's calmed down, I'll have Mr Filch restore her."
(Prisoner of Azkaban).
What was Dumbledore expecting Filch to do here? As we know, Filch is a squib. He can't perform any magic.
Now fixing the Fat Lady would've been a relatively easy task for a qualified wizard or witch to do. A simple bit of Reparo and Bob's your uncle. All that was ailing the Fat Lady were a few meagre slash wounds. In and of themselves they were easily fixed.
But what could Filch do about it? Try to patch her up with some Spellotape? Wouldn't he have had to have called upon another adult who could use magic to help him anyway? Why leave Filch to struggle in vain? Or is this just another example of Dumbledore cruelly forcing the non-magical members of staff to do all the heavy lifting (like when Hagrid had to drag all the Christmas trees in from the grounds by hand)?
Edit: I found the following exerpt from the Fat Lady's return to Gryffindor tower, which throws some further light on the incident.
Sir Cadogan had been sacked. His portrait had been taken back to its lonely landing on the seventh floor, and the Fat Lady was back. She had been expertly restored, but was still extremely nervous, and had only agreed to return to her job on condition that she was given extra protection.
(Prisoner of Azkaban, Chapter 14, Snape's Grudge).
Is her being "expertly restored" consistent with Filch doing the job?