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.
U.S., allies conduct 20 air strikes in Syria and Iraq against ISIS, says U.S. military (Reuters)
from the article: Israel Police chief urges state to appeal Olmert's acquittal