There's nothing wrong with open-source solutions for voting. The question is whether any system which does not record votes indelibly on a medium that a ordinary person can examine should be trusted.
If a system has voters select entries on a touch-screen system which prints their choices on an optically-scannable ballot, I see nothing wrong with using open-source software on such a machine though the possibility of 'cheating' would be pretty minimal since anyone could examine the ballot printed by the machine and ensure it was accurate.
Likewise, the tabulation system could be open-source since its inputs and outputs would be entirely testable. If each ballot were tagged with a unique machine-readable identifier sometime after it was cast, the ballots could be run through two machines, using different hardware and software, and the results compared. Any ballots whose interpretation didn't match on the two counts could be mechanically separated for examination.
The key requirements for a good voting system should be (1) votes should be recorded on an indelible medium. Punched tape is fine. Printed cards are fine. Flash memory is not; (2) an ordinary person should be able to examine the system and confirm that votes are indeed recorded as indicated; (3) ballots should be designed so that (a) any alteration to a validly cast ballot will render it invalid; and (b) there is no way an invalid ballot can legitimately enter the ballot stream.
Unfortunately, even though these requirements seem obvious to me, many voting-system designers don't seem to care about them.