MacBook Pro 13" Unibody Mid 2009 Hard Drive
Quick tip: Once you connect the new battery, try to carefully peel off the very small rubber looking insulation on top of the battery connector of the old battery and stick it back on top of the battery connector of the new battery. Once done, only then do you screw back on the metal battery connector bracket.
I didn't do this the first time I replaced the battery and noticed that call quality was a bit choppy. I was trying to think what might be causing the issue and guessed that this insulation must be doing something to insulate the connector from the metal bracket. I opened it up again and put on the insulation and it appears that the usual good call quality has now returned!