The only companion mishap I've encountered so far is the Veronica bug.
At the end of her personal quest, she breaks and stops following you no matter what.
Luckily there's a fix.
Though I can't say much more without spoiling.
I have to say that I really like the companions. They have much more personality and story to them than the ones in FO3.
And I have a hard time deciding which ones (of the ones I've encountered so far, that is -- Boone, Veronica, and Cass) I want to take with me.
Yeah, there are mods to allow you to have multiple companions... And while it might seem cool to have a little army following you around.. you'd end up doing less and less fighting. Ammo will build up and before you know it.. you're overencumbered.
Oh... I lost my train of thought.
Anyway, Eddie. Well. I've had him from practically the start of the game and have never once lost him. He's the good one.