There was a streetlight near me that would be running during the day but shut off by night for some reason. It's photocell controlled and it's on a circuit shared with a few dozen other streetlights (all of which worked fine).

I'm curious as to why this was happening, my only two guesses are either the photocell is broken or it's a different type of photocell.

Wrong photocell type...

On at day and off at night is a mude used normally with tunnel lights, where it makes sure there is not too sharp contrast between the open road and the road in the tunnel, so it turns additional lights around the tunnel entry/exit ends during the bright day. This uses remote photocells, but the cells would have the same form factor (to share the same components with normal street lights to save cost.
So apparently someone put by mistake such device into a normal street light...

Oddly enough, a motion sensor light on my Uncle's house has a broken motion sensor with an integrated photocell that does that.

@FL lover

If the "NC" contact of the photocell relay was available inside the light, maybe it was connected (miswired from the factory)

Otherwise...

The photocell part of smal lights is typically an LDR, transistor based amplifier (made with 1..3 transistors and a bunch of resistors, all discrete components), and a relay

Each transistor stage in the amplifier acts as inverter - that is, a "low" signal in the input of the stage makes "high" signal in the output. What if, by any chance, one of the stages got somehow bypassed - For example, a spot of rust (from Water ingress) shorting the Base and Collector of a transistor together while the emitter lead failed open circuit ?

If the amplifier circuit will still be able to work at all (and not rendered inoperable by getting into an unusable DC working point for example), each bypassed stage inverts the sign of the gain, so would invert the working logic...

There was an LMI/McGraw-Edison Unistyle-400 down the street from me when I was a kid that did this...always made me chuckle.   

When I was in university, a bout of lighting had that effect on timer switches (not sure if they were digital or not). Maintenance people didn't work at night, so they assumed the lights were simply day burners and would get around to fixing it sometimes. Then I talked to one of my coworkers at my campus job, and she sat on the health and safety committee. When I mentioned the lights were off at night (she never worked at night either), she was surprised but she let maintenance know and they reset the time clocks.

Yes, in this case, the reverse photocell model is the most plausible. Maintenance workers were too much in a hurry and didn't care if it was a "day burner", and let it like that, probably with a 'promise' of coming back to troubleshoot further. Or maybe stockroom employees ordered the wrong type of photocell.