No, public election of judges does not improve the quality of judges, because the public is too uninformed about the candidates. It takes a unique set of qualifications to make a good judge. The public is likely to vote for whomever is nice, or charismatic. There are too many judges that aren't smart enough to do the job.
Judges are supposed to be impartial. The lawyers present sides, and the judge presides impartially. When judges are elected, though, they have to consider their popularity. They may feel pressured to side with majority opinion, in order to win a majority of the votes. That's why the founders set up the Supreme Court so all justices serve for life. All judges should, so they stand a better chance of being truly impartial.