I strongly doubt that the business records exception or many of the other hearsay exceptions will apply to tweets . . . but the exceptions contained in Rules 803(1) and 803(2) just might. ...

I don’t think these are the only exceptions that could be used for tweets. Under Rule 803(3) of the Federal Rules of Evidence, “[a] statement of the declarant's then existing state of mind, emotion, sensation, or physical condition . . . but not including a statement of memory or belief to prove the fact remembered or believed unless it relates to the execution, revocation, identification, or terms of declarant's will” is not excluded by the default hearsay rule. According to the Advisory Committee, this is “essentially a specialized application” of the present sense impression exception. Advisory Committee Federal Rules of Rule 803(3). The Committee also noted that excluding statements of memory or belief is “necessary to avoid the virtual destruction of the hearsay rule, which would otherwise result from allowing state of mind, provable by a hearsay statement, to serve as the basis” for inferring the event which “produced the state of mind.”

It seems to me Rule 803(3) may be a better fit for tweets than the other two rules. As a federal judge noted, “Rule 803(3) is particularly useful when trying to admit e-mail, a medium of communication that seems particularly prone to candid, perhaps  too-candid, statements of the declarant's state of mind, feelings,emotions, and motives.” Lorraine v. Markel American Insurance Co., 241 F.R.D. 534 (U.S. District Court for the District of Maryland 2007). And at least one court relied on this exception in ruling that emails were admissible in a federal criminal prosecution. U.S. v. Safavian, 435 F. Supp.2d 36 (U.S. District Court for the District of Columbia 2006).