I recently replaced the front shifter cable on my wife's bike. I first put the chain on the middle cog in the front, and adjusted the rear shifter cable tension using the barrel adjuster to make sure each click of the shifter resulted in a shift of one gear both up and down. I then installed the new front cable, and adjusted its tension.
Fast foward a couple weeks, and the front derailleur rubs against the chain when it's on the largest cog. Totally expected. So I was about to tweak that when my wife mentions that the rear derailleur is not quite working right either.
I place the chain on the smallest front cog, and it shifts just fine. The middle one is a little hesitant, but each click on the shifter does shift a gear. On the largest front one, however, there's a gear in the middle of the back where there's a click, no shift, then the next click shifts two gears. I can still get into that gear, but only from the lower (larger) side. If I adjust the rear derailleur tension so it works on the largest front cog, it starts to act up on the smallest.
I tried looking at the alignment, and to my (untrained and inexperienced) eye, it looks like the derailleur is hanging pretty much straight down from the frame. Any other ideas of what to troubleshoot?