An encounter between Dan and "Anne" in Ep. 29, when she repeatedly denied being her and she was playing single mom to Creepy Child Uri, whose telekinetic powers and propensity to throw tantrums put everybody (even his mom) in danger. That was Yuriko Hishimi guest starring alright, just not Anne, or so we're led to think.
The Ultra brothers' joint beam attack on Leo in Ep. 38, after Leo stood up for "Astra" aka Alien Babaloo, who had stolen the Ultra Key while the real one was in a frozen rock in space.
A few victims of collateral damage throughout, like Tohru's father and Gen's photographer friend.
Leo's dismemberment and temporary death. The writers rub salt in the viewer's wounds by having Leo say farewell to Tohru telepathicallyin the middle of the night.
Gen's frustration and anger over Alien Magma's attacks on Earth after blowing up Planet L-77.
Gen's disappearance in the first part of Episode 4. Dan himself shed a tear...