Speaking of that tweet, Trump's team claims that lawyer wrote it and social media guy posted it without Trump knowing. In my reading of that statement, it's meant to keep the tweet from being admissible as an opposing party statement. Essentially, that means that in a criminal case, the government can use any statement that the defendant made.
However, rule 801(d)(2)(b) might be important. That allows statement that a defendant has "manifested that it adopted or believed to be true." I think by leaving the tweet up on his own account after he knows about it is "adopting" it under the rule.
I've never dealt with twitter, but search warrants and subpoenas can sometimes pinpoint information on facebook and instagram. I bet Mueller and his team are working on nailing down the source of the tweet.