Remiss means someone who does not care/ failing in what duty requires; slipshod which means careless, is thus the right choice here.  The meanings of the other words are highlighted below:

Coarse: Of textures that are rough to the touch or substances consisting of relatively large particles

Ominous: Threatening or foreshadowing evil or tragic developments

Dinghy: A small boat of shallow draft with cross thwarts for seats and rowlocks for oars with which it is propelled