There were a few, in hindsight. The first was when I was in labour with our son - and ex decided to vanish off to have a nap in the car, because he was tired... then went home to his parents house. He missed our son's birth completely.
The second was when he refused to pick up my frantic calls when son was 3 days old, because the midwife was concerned his sacral dimple wasn't closed, and the GP wouldn't see him unless his birth had been registered. Midwife was adamant it might be an emergency, so we ended up with an emergency registrar appointment... and my ex's name didn't go down on the birth certificate (not married, but by then, even if we had of been, I don't think I'd have said so). This caused him to tantrum about it, when he realised - a year later. Son is now 16, and there's still a blank space under "Father's details" - because ex can't be arsed to sort it out. (Son's dimple was closed, incidentally, just very deep?)
Then, when son was 2, and innocently telling me about "Daddy's new friend" after their father/son afternoons out, denouncing him as a liar. Son is on the spectrum and simply doesn't know how to lie. Certainly not at 2 years old. Ex, on the other hand...!
Then, when son was 4, taking him off out for the day - before ringing me to tell him that his "new friend" had given birth to their baby that morning, and he was taking son to the SCBU to meet her (son ended up having nightmares about the place for months afterwards).
We'd known each other since we were 11, been together on/off since 14, hooked up properly when we were 22 after he'd helped hold me together following a very abusive relationship/surprise pregnancy. My daughter adored him, we had a shared history together, I got on well with his family... but in hindsight, because of that shared history, and how vulnerable I was at the time we hooked up, it was a disaster waiting to happen. I refused to allow him to move in, because my daughter came first; he went travelling regularly and made jokes about drugs to wind me up (he does this to son, too). The main thing I'll never forgive him for though, is the deceit. The betrayal of my children. The way he denounced our son as a liar.
He's married to the OW now, and I know from mutual friends that he's cheated on her at least 3 times that they know of. I've not spoken to him since son was 5. Son refuses to see him, now he's old enough to have his choices listened to. Yet ex is apparently still "Mr Nice Guy" and "the life and soul of every party...". I really don't envy his wife.