There is no doubt that genuinely guilty people have been acquitted, and a second trial handled better and with better attention to the evidence may produce a just result. A lot of people are pointing that out and it's true. That's the upside of this.
The downside is that the possibility of getting more than one crack at it may encourage a less than completely thorough approach the first time. As you say, it allows the prosecution to see the defence and take evasive action the second time. And it allows the state to pursue an individual maliciously and repeatedly.
It also introduces the danger that after an acquittal the police will not do what they should do, which is re-examine the case from the ground up and see if they have evidence pointing to someone else who can be charged (as was done after the acquittals of the first people charged for the murder of Damilola Taylor), but might rather continue to obsess over their original case trying to find some more evidence.
I suspect that if double jeopardy had been permitted at the time of the original Damilola Taylor acquittal, the real murderers might never have been found. We might still be witnessing the unedifying spectacle of the police announcing that they weren't looking for anyone else and setting out to try the first lot of people again.
And as I said, look how the mere threat has been used to terrify Lamin Fhimah. They've got nothing on him, and if pressed will say that they have no immediate plans to charge him for a second time, but there has been a continual drip drip of stories indicating that this is what they want to do. For a time, every tabloid story about the abolition of the prohibition on double jeopardy was headed up with the assertion "man acquitted of Lockerbie bombing could be re-tried". This is oppressive.
Rolfe.