Now, I know I need to learn analog stuff, but I only want to learn a bit more than the minimal amount as far as analog goes (unless I can get myself interested in it).
All digital signals are sent along analog wires, with their finite and nonzero resistance, capacitance, and inductance, and the associated propensity to radiate EM waves, as well as to capture EM radiation. The lines are driven by analog circuits, with limited slew rates, limited output voltages and currents, etc. If you can ignore the analog details and simply treat things as ones and zeros, you should heartily thank the designer(s) somewhere along the way who did a good job of handling those analog details for you.
Many of the nasty problems you run into in a digital design are really analog problems. Crosstalk, impedance mismatches, RFI susceptibility, etc. can make a digital device "flaky". If you don't have the analog background, when your digital circuits start misbehaving, you won't have the necessary tools to diagnose and fix the problems.
Even if you're only designing boards for digital products, you've got to know enough about analog to keep yourself out of the danger zones. It may help if you run everything really slowly, but that's not a good strategy for high performance.
A few rules of thumb may keep you mostly out of trouble if you're treading well worn ground making an ARM board that's similar to existing ARM boards. But to do significant design, you should gain at least a reasonable familiarity with inductance, capacitance, transmission lines, simple analog filters, impedance, frequency response, etc. That's especially true if you want that ARM board to interface with the analog world.
I've been out of the introductory literature too long to recommend a specific introductory book, though. Perhaps "The Art of Electronics", by Horowitz and Hill, but I'm not sure if that's what you're looking for.