Dzhokar Tsarnaev was a United States citizen at the time he was picked up for questioning. It was known that he would be questioned extensively and would probably have to go to court at some point. Per U.S. laws, Tsarnaev should have been mirandized. If not mirandized, everything Tsarnaev said should be inadmissible in court.
Should the FBI have mirandized Tsarnaev? Why did they not read him his rights. Had they done so, would not the case against him be much more solid? Is other more evidence that incriminates him even without his own statements? It would seem that since he was not mirandized the state may have a much harder time getting a conviction. Allegedly he talked a lot initially, even mentioning that he and his brother intended to make the New York City Marathon their next target and admitting to be a jihadist. But if he was not read his rights the admissibility as evidence of anything he disclosed may not be guaranteed. Possibly the FBI was thrown off its game by the state of his health? But they know the rules. It is not like them to neglect to mirandize. Hopefully there is more to build the case on. But it does appear, to the uninitiated at least, that not mirandizing Tsarnaev was a serious error.