When I use the multiple option in a select dropdown - safari runs into weird issues. When I select an option and say Done, the dropdown goes back to showing \'0 items\'. But
'Multiple select' bugs in Safari in iOS 7.0.3 on the iPhone have been reported by others, as well, on Apple's discussion forums; e.g.:
https://discussions.apple.com/message/23745665#23745665
https://discussions.apple.com/message/23607781#23607781
Since it's Apple that will need to fix this, the consensus approach for what you can do to help facilitate resolution of this issue, per posts on those two discussion threads, is to: