"To permit a second trial after an acquittal, however mistaken the acquittal may have been, would present an unacceptably high risk that the Government, with its vastly superior resources, might wear down the defendant so that 'even though innocent he may be found guilty"
This from Green v United States, 355 U.S. 184, 188 (1957) was quoted in Evans v Michigan
USSC No 11-1327, 20 February 2013. Here an acquittal had been directed at trial although on grounds that were plainly wrong. The acquittal was nevertheless valid and effective to invoke the rule against double jeopardy.
Evans highlights the distinction between procedural terminations of trials and findings on the merits. A procedural termination is not an acquittal because it is not a finding on the merits. A procedural termination avoids the defendant being in jeopardy of a conviction. A properly granted mistrial does not give rise to an expectation of finality.
In Evans the judge ruled at the close of the prosecution case that the evidence so far adduced was insufficient to convict the defendant. The judge wrongly thought that the relevant law of arson required proof that a particular building was not a dwelling, and directed a verdict of not guilty accordingly. This was held to have been a ruling on the merits and a bar to a retrial.
You can see that this is a bit silly. We saw an analogous sort of silliness in R v Taylor  NZCA 558, discussed here on 18 December 2008. Taylor was applied in Connolly v R  NZCA 129 at -.
It is silly because it turns on the stage of a trial at which an objection is taken: has jeopardy of conviction arisen? If the prosecution case has been closed, then yes, there is jeopardy, as in Evans. But what if, after the jury had been selected and the trial begun, the defence had objected that on the basis of the evidence that the prosecutor intended to call there was no proof of an element of the offence, and before any evidence was called the judge ruled that the prosecutor needed that evidence, and the prosecutor confirmed it would not be adduced, and the judge then directed an acquittal? Would jeopardy have arisen? Is this a procedural termination? The position as it would inevitably be if the prosecution case proceeded to closure is being anticipated. Why wait until closure of the case? Yet the authorities suggest that this would be a procedural termination, not a decision on the merits.
Is there a sensible policy behind treating directions that are obviously wrong in law as nevertheless giving rise to legally effective acquittals? If there is, is it consistent with whatever policy might justify distinguishing between procedural dismissals and rulings on the merits?