Regarding the possible mode-hopping:
Normally green DPSS lasers are designed to produce a beam that when projected on a surface produces one dot, which is brightest in the center and less intense as you move away from the center of the dot. When a laser mode-hops, it tends to form a beam that produces more than one spot, or a blob-like spot instead of the normal clean round spot. This will cause the lines from you projector to look like yours do. This is an internal problem with the laser, and the quickest solution is to replace it. Repairing a DPSS laser that is out of alignment is complex and is not recommended unless you're willing to do a LOT of reading and asking of questions..
Here's a couple of articles about laser modes and mode-hopping:
http://en.wikipedia.org/wiki/Transverse_mode
http://www.rp-photonics.com/mode_hopping.html