paper trails and vote counting
If a paper trail is produced along with the electronic votes, then it can be used as a sample test of the veracity of the electronic count, as well as for any re-count.
Election observers could have the right to choose which machines' paper trails were collated with the electronic votes they registered. Of course with human counted voting, you rarely get the same numbers twice, and with machine counted voting, you are relying on the machines.
However, in the USA where politicians get to decide on the constituency boundaries (Gerrymander comes from a US politician's name, man who designed the constituency boundaries to ensure he got elected), the electoral system has other equally or even more serious problems.
At least in the UK we have an independent electoral commission, but how effective they are at ensuring fairness, I do not know.