@mrmister So I checked the optics and you are right - the only thing in front of a laser diode is a spherical lens.
@Zax Lens looks fine, at least it has no visible imperfections. I'll try contacting seller (in my case that would be Banggood) and see what have to say. I went through most of Sam's Laser FAQ, especially Beam Characteristics and Multimode Diodes sections to educate myself and perhaps find a solution.
Zax, or anyone else reading this, could you please post a picture of your output beam? With a comment if it was like this from the very beginning or you used some tricks to correct it.
Edit: And one more thing - do you think it would be beneficial to open this kind of discussion also over at benboxlaser.us forums? I see some people are in both locations anyway.