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Today I noticed some exposed copper rectangles on the bottom of an mbed NXP LPC1768 dev board. They don't look like they're meant for components. I think they may just be test points, but I'm curious if there's another answer.

Here's an image of the board with the copper rectangles circled in red:

I'm not sure what the mbed interface chip is. Googling it suggests that it's proprietary. I can't tell where the traces are going.

Those look like test pads and seem large enough for soldering a wired connection.

An educated guess would be JTAG (TCK, TDI, TDO, TMS) plus VCC and GND. VCC and GND could be verified with a multimeter.

Note that the interface chip is also a programmable microcontroller, and thus needs JTAG or SWD for production programming.

NXP has the schematic for this board, it looks like those pads make up a programming interface for that chip, which as you say is likely custom in some way.

Sometimes, you see such elements on microwave boards on the microwave lines – then, they serve the purpose of being a capacitive or reactive component (or both); but since this board definitely doesn't look like an upper-GHz RF board:

These are almost certainly test points.