I'm getting ahead of the anxieties about a COVID-19 vaccine. Note that I have no real concerns about a vaccine, and expect an effective and safe one to be developed. This is just what I expect to see on social media and the press:
The rollout is too slow. This is going to be a very likely criticism. "We waited X months waiting for it, why is it taking so long to get to people?" will be the line.
Too fast. This isn't very likely. But maybe the side-effects will be too scary, so people will say it was rolled out too fast.
Too dangerous. A variation of the above.
Doesn’t work. "Why are people still getting COVID-19 if there's a vaccine?" Remember, the answer is either because that person wasn't vaccinated, or the vaccine helped but wasn't 100% effective (the flu vaccine, for example, is not 100% effective, but it's by and large popular).
Unevenly distributed, especially amongst income levels, but other demographics, like gender and race.
Rich people/VIPs jumping the line. This will be a gotcha moment. "Why are politicians/Hollywood actors/rich people jumping the line?" will be the refrain.
Scams, especially things that claim to be vaccines or cures.
Anti-vaxxers are a given. They seemed a bit muted during the pandemic, possibly because almost everybody was affected by the shutdowns/lockdowns in some way and maybe people who wouldn't otherwise welcome a vaccine are accepting of this one.
They not only don't work, but make things worse (almost to the tune of the song by The Verve)