Lines Forming in OpenStreetmap

I tested a little: This behaviour appeared when I had enlarged the whole page size to 110% or more in Firefox. Maybe this is your issue, too?

The white stripe/pixels issue in the rendering is well known problem. The issue is a consequence of many factors in use like the scale factor, the rounding strategy, the processor's precision, the viewport's position just to mention some. Therefore the white stripes in the question comes and goes randomly on different machines, displays, browsers, pan-positions and some times it is difficult to repeat them. Here is an example created on my HP/WIN8/64bits machine (December 29.)

To understand the problem in cases like mentioned by malenki (scale factor 1.1) is quite easy (sometimes an image row/column x is rounded to row/column n-1 on the display while the x+1 to n+1) and these kind of white stripes are very well handled by any private/kernel renderers. The issue is slightly more complicated when the scale factor is 1.0 and the raster image to display is tiled. Namely, the tiles are individual independent images and their edge-to-edge alignment is provided by their (corner) position co-ordinates (given directly/indirectly in the corresponding profile). Anyway, these co-ordinates have to be transformed to the tile's display integer start position. So, because of the mentioned reasons, it may happen that this start display position is for one pixel away from the last rendered row/column of the previously rendered tile.
With a robust renderer this should never happen. There are at least two major strategies to avoid the white stripes. One, for any tiles in rendering (maybe except those in the last row and column) the last raster row and column is rendered once more into the next display row and column. Next, especially in case of uniform tiles, the tiles are positioned/selected in such a way that the corresponding position co-ordinates are exact integer multiplications of the corresponding tile-dimension.

Thank you for your report! However, I have no such problems in my Firefox (version 26.0). Could you please try with a fresh profile or under a different user account or easily on another computer? You could also try to switch off zooming or any addons (if existent). You could also try to reload the page without caching in your browser: hit Ctrl+F5 while being on http://www.osm.org.

To explain: those white lines on your map display are exactly between the map's bitmap tiles. One example (compare the borders with your white lines).