Without a ratified constitution, true protections are unavailable. The protection from double-jeprody would be a great place to start. In the case of Olmert, just because the prosecution presented a weak case shouldn't give them the ability to have a second chance to get it right... Or worse, judge or court shop what was originally a correct judgement.
Woman wounded by stones thrown toward her car near Jerusalem (Haaretz)
from the article: Israel Police chief urges state to appeal Olmert's acquittal