1. Shows getting cancelled is now a long, slow, terrible death - because everyone ASSUMES Netflix will just pick up EVERYTHING.
There's no such thing as a show dying a natural death anymore - the instant ANYTHING gets cancelled by a TV network, the internet gets itself worked up over the potential of Netflix (or some other streaming service) picking it up. And this isn't just for beloved cult shows - it's pretty much ANYTHING that has any amount of fans. There was a while when they were going to reboot the sitcom Coach, which has been off the air for about 20 years. They've picked up shows no one cares about like Longmire.
So whenever ANYTHING is cancelled, the internet works itself up in a tizzy over who can pick it up, and that goes on for months. No shows are allowed to die a clean death anymore - it's a long, drawn out process that USUALLY ends in the same level of disappointment.
2. They're going to keep bringing back shows and they're going to be bad.
This kinda sucks, because nothing's allowed to die a noble death anymore - used to be things would get cancelled before their time, and would (as a result) be remembered fondly, since it never got a chance to get bad. If Firefly were cancelled today, it would've been picked up by Crackle and ran for another 9 seasons, the final 3 of which would have been awful. Did anyone watch the 4th season of Arrested Development or the Yahoo! 6th season of Community and think "that's their best work!"? Probably not.
The point is - sometimes it's okay to let things get canceled, but Netflix is basically Pet Semetary for dead shows. And sometimes....dead is better.
3. No one's being forced to watch random stuff because nothing else is on
As a kid, I was stuck watching a lot of stuff I wouldn't have necessarily chosen, since it fell out of my comfort zone of "cartoons that prominently featured Sonic the Hedgehog." See, it used to be that there were limited options in TV watching, so you were sometimes stuck watching marathons of Gilligan's Island or reruns of L.A. Law.
The problem with having an insane amount of options provided by Netflix at all times is you never, ever have to leave your comfort zone. Sometimes it's good to be forced to watch something you thought you would hate or wouldn't interest you, because you find out it's actually a totally new thing you're into. And that's not to say you can't do it now - of course you can! And you have even more options! But most people won't - they'll stick to rewatching reruns of It's Always Sunny In Philadelphia instead of giving Trailer Park Boys a shot (especially because the early episodes of TPB aren't really their strongest, so you may bow out before the show has a chance to sink its hooks in you). Too many choices can be suffocating and overwhelming - and Netflix has made picking something to watch way, way too difficult.
4. Binge-watching makes me incapable of distinguishing individual episodes of anything
The relatively new concept of "binge watching" is sorta great - it's incredible to just have a complete season dropped on your lap, so you and your significant other can just spend a weekend blasting through a super-well-produced drama about sleazy politicians who are blind and meet Aziz Ansari's parents, or something (things tend to run together a little when binge-watching).
Oh yeah, but that's the problem. When you consume an entire season of TV in one weekend, things grow less distinct. You remember individual episodes a lot less, since you didn't have a week to think about the events of the last episode and wonder what would happen next. You didn't have a chance to talk to friends and co-workers about how great that last episode was, or how you had a theory about one character. You can only discuss shows in terms of the entire season, never really individual episodes - which is what TV is truly about. There's no time to theorize online or get super-attached to characters, since you only spend any time with them for like 2 days out of the year.
5. Netflix is everything I ever dreamed of for TV watching and I don't know how to deal with happiness
I'm a bitter, cynical adult, and Netflix (and pretty much every streaming video service) is everything I could dream of - no commercials, tons of shows and movies from across every spectrum of content, daring new shows that may never have been made for network television (Netflix's Marvel shows, Amazon's The Man In High Castle), and it's cheaper than any cable package could ever hope to be. It's too wonderful - it feels like a dream, and accepting that is hard.
Thank you, Netflix, you life-ruining sonuvabitch.