" Not to mention that former prime minister Yulia Tymoshenko and Yuri Lutsenko, two prominent opposition political leaders, have been imprisoned following trials that were widely criticized as politically motivated. While election day was largely peaceful, there have been allegations of fraud in the voting process and tabulation."
I guess "while" would be refering to simultaneous action in the past? It doesn't say that allegations were after election day.
No, that isn't the meaning of 'while' here. Compare: 'While elections in 2008 were violent, this year they were largely peaceful."