A family dog that died before the show starts is briefly mentioned (and seen in a flashback) but no dogs die throughout the course of the first 7 episodes.
S1E5: Ron gets forced at gunpoint into cheating on his wife with another woman. The context is a misunderstanding (a man thinks Ron was hired to catch him cheating on his own wife) that's played for laughs, but it's pretty unsettling.
(Spoiler alert) Multiple times through the show the character Mike is heard listening to p*rn, at the end of episode 5 he’s watching one and a man with a fake p*mid is given oral sex by a woman. Pretty uh, fake, but also pretty gross lol