Why did the clocks move one hour backwards when Rin summoned Archer? At the beginning of Ufotable's UBW adaptation, on the day Rin was going to summon Archer, the clocks happened to have moved backwards by one hour. She considered that it may have been her father's doing.

Why did the clocks move one hour backwards?
The explanation is kind of dumb. 

The day before Rin summoned Archer, she was rummaging through her father's effects in hopes of finding stuff that would be useful for the summoning. One of the things she found was the box containing the pendant (and, at least per the depiction in UBW 2014, the catalyst for Gilgamesh), protected by a magical MacGuffin that, when activated, makes clocks go wonky and apparently rewind by one hour. She activated the MacGuffin. The clocks rewound in two half-hour increments. She only noticed one of the half-hour increments. The end.

Nasu later stated in an interview (in Complete Material 3) that this was apparently an intentional "test"-of-sorts on Tokiomi's part, the idea being that if she couldn't handle a minor issue like this, she wasn't cut out to be in the war. 

This makes no chronological sense, because Tokiomi likely never expected Rin to be in the war in the first place (Tokiomi would have expected the fifth war to take place around 2060 or so, by which time Rin would have had descendants rather more sprightly than she), but there you have it.