The magnitude of the emissions. We are putting tens of billions of tons of CO2 in the atmosphere per year. Even assuming the filtering process is very efficient (net-carbon negative) where do we store that in the blimp? How many blimps would we need?

As a thought experiment - look at the average car - a Toyota Camry for example. That car emits 206 grams per kilometer. Over the course of the car's lifetime (about 200 thousand kilometers or so) that's 41 thousand kilograms of CO2. For one family car.