My I2C component was the ADXL343, which I didn't realize was a terrible choice for a first time go at this (check out week 9 for a better explanation). Basically, the component is too small for the Carvera, our CNC machine, to actually mill out the pads.

Here is the result of the milling process. In the PCB design, I didn't notice this at first (mainly because I wasn't aware), but the ADXL343 pads are interesecting by the really thin red line. This would have risen the alarm bells only if I used the [rules checker] function in KiCad.

In the physical board, you can see the pads conjoined into one island.