You're right, that is a weird pinout.
You could drive it with a PIC easily enough. In order to get a consistent brightness, strobe the LEDs that share a pin alternately, and also strobe the unshared-pin LEDs at a 50% duty cycle. So you'd have 2 cycles:
Cycle 1: B,E,G,J are on.
Cycle 2: C,F,H,K are on.
For the individual LEDs, pick a cycle to light those up on. You could light all of them on cycle 1 for example, or put half of them on cycle 1 and half on cycle 2. So, for example:
Cycle 1: A,B,E,G,J,I are on.
Cycle 2: C,D,F,H,K,L are on.
Without strobing, you'd have to use a constant-current source to run the pairs of LEDs in series, or individual LEDs in the case where one needs to be lit and another unlit, to get a consistent brightness. The strobing method is much easier.
You'd think they would have just given all the LEDs a common cathode, or a common anode, thus only needing 13 pins for 12 LEDs. That arrangement is much easier to drive as well.