This is a list of issues, by browser, that the VisualEditor team would like to see the browser manufacturers correct. It's sort of a mix of feature requests and bug reports. Include JSFiddles when possible.
Internet Explorer 
- Base64 encoded 1x1 transparent GIF renders red in IE10 Consumer Preview when used as img src (used in phantoms)
- Trying to recreate conditions to trigger JSFiddle. Will have more progress in January.
- Contenteditable="false" within Contenteditable="true" is still editable. JSFiddle
- MouseEvent.detail is improperly implemented. JSFiddle
- Cannot hide resize handles on images
Mobile Safari 
- Shake to undo
- No way to prevent (should be able to prevent)
- No events fired (if shake to undo is not prevented, the undo event should be present and hijackable)
- No way to disable spellcheck or autocorrect in Contenteditable (works in form fields with proper attributes)