Does this Macbook Air need a new battery? Well, yes: especially when you see swollen Li-Po (Lithium Polymer) pouches like the ones to the right in the photo. Another symptom of a swelling Macbook battery is that the trackpad no longer clicks: the battery is swelling up against the trackpad from underneath.
When I installed the new battery and tightened down the screws on the underside once the new battery fully charged it swelled slightly and the trackpad wouldn't click. I had to loosen the screws slightly to get it to work. I ended up returning that replacement battery as defective, the new, new battery doesn't seem to have the same issue.