cleaning the lens won't help the two-mode issue, but to clean the lens, I use 91% isopropyl and a cotton swab, and spin the swab with a very light touch, enough to saturate the area. Works fine on glass lenses, haven't tried on acrylics yet.
Try to get the cleanest swab you can, because if any damage is done to the lens, it is not from the alcohol or cotton, but from the speck of contaminant that may have snarled itself into the cotton.
Temperature can often affect alignment. If they get it all lined up at the factory, but it's 90F in there, then when it gets to you and you keep your house at 70F, that could be enough for expansion of the metal mounts to move ever so slightly out of alignment. Now, that was just an example with random temperatures, but you might see if it does the same thing if kept in your pocket to warm up a bit before turning it on, or leaving it on the windowsill to cool it down before turning it on.
