I can't speak to the issues that people are running into when they reach large scale, but I run a small app with two dynos and we've been having issues with H12 request timeout errors for weeks now. This has been bringing down our production app for periods of about fifteen minutes almost daily.
I've been completely disappointed with Heroku's support so far. First they obviously skimmed my support request and provided a canned response that was completely off base. Their next response didn't come for four days and only after I called their sales team to see what I could do to get better support. Their only option is a $1k / mo support contract. If you're running a mission critical app, I'd think twice before choosing Heroku.