White lines between map tiles

You've got more wrong than that - the scale bar is wrong in this shot as well. My guess is invasive CSS - can you drop a link to the page, or check out certain elements with FireBug to see if there are styles cascading down to these, adding incorrect margins, probably.

re-open if this is still broken.

Definitely invasive css. Your theme is "helpfully" adding margins to img tags. you can override this with .openlayers-map img{ margin:0px }