season 1 annoyances
I'm frustrated how easily a single cop took over a destroyer with 250 people on it (and presumably 250 guns).. that is just lazy writing.
season 2 annoyances
The absolute moral kerfuffle the main cast got into because the Philadelphia authorities were euthanizing the infected seemed very out of character. These are military members, and they understand hard choices, now that there is a vaccine the equation changes, but the absolute black and white "your evil" take they have doesn't fit apocalypse survivors.