The stupidity and the lack of suspense
Those are the two biggest problems in this movie. I have a feeling that Ti West had a pretty good idea about how the movie would start, up to a point where they arrive in the house and how it will end. I think he wasn't sure how to connect the two properly so we got some problems.
The villains in the movie are pretty stupid. Their whole plan depends on the fact that she needs to order a pizza while they pretend to leave and...wait I guess.
They already have her right where they want her, so why don't they just grab her, or put the same drugs in the glass of water or something?
Some will say "But what if she's not thirsty?". Well, guys, what if she just doesn't want to order pizza? What if she doesn't feel like eating?
It's less risky than just waiting and hope she'll order a pizza. Plus, they're on a time limit, so they should be in a hurry and not put their whole plan at a huge risk like that.
So she does order a pizza, which was a huge luck on their part, but when they tie her up they don't even do it properly and let her get away. She manages to escape from a room full of crazy cultists.
And that's what the movie relies on to keep the plot going, the stupidity.
Even the main character is stupid. They lie to her about who she has to babysit and tell her they don't have enough money to pay her and her friend, then later offer her more money.
She doesn't find all that lying and just weird behavior in general from them suspicious.
I have a feeling the bad guys have such a stupid plan is because they need to make the movie longer. The scenes where she's listening to the music etc. feel like padding. Ti West needs to make a movie longer somehow, so cultists have to pretend to leave.
Now, people talk about suspense being built here but it's just Sam exploring the house. She's not in any danger really, there's nobody stalking her in the background, preparing to kill her at any moment. They're waiting for her to order a pizza.
And with flaws like these the whole "It looks like an older movie" thing just starts to feel like a gimmick. I know that probably wasn't the director's intention, he just wanted to make a movie in the 70's/80's style but he didn't do such a good job at it. So, without that whole look this movie wouldn't be talked about as much and would probably be forgotten quickly.