Earlier quoted context omitted.
Unilateral contracts are a thing, when one party makes an offer that is only accepted by performance. As the offeror, Disney can invite acceptance of their contract however they want, including via replying to their tweet with a special hashtag. They made the requirements pretty clear and stringent enough that I very much doubt anyone is at risk of accidentally entering into that contract, but if that does happen, th…
It has happened. People replying to the tweet, with the hashtag, but trying to discuss the intent with Disney are clearly not attempting to enter into the contract. The problem is Disney co-opting two regular parts of Twitter's service, and then claiming that represents a Disney service. It isn't, and can clearly be used for purposes beyond establishing a contract.
You can set up a phone line or P.O box with the same terms of service agreement. Twitter is not sacred. You can call that "co-opting" those services I suppose, but I don't see why that's a bad thing. Services exist to be used.
Disney is going to use some common sense when reviewing these tweets and filter out the trolls and people disputing the terms. They are not out here trying to trap helpless children into a contract, just make some marketing materials. Again, this is not the first time this has been done and is not controversial. Maybe I underestimated the number of troll tweets, but I'm sure Disney will figure it out just fine.