I have found the bug in version 0.6.3 of the Recent Posts Slider. For my WordPress installation (in a subdomain), the following worked. YRMV.
Around lines 459 and 471 (same code appears twice, replace both instances!), look for this original code:
$rps_img_src_path = "/".$post_details[$p]['post_first_img']['0'];
$rps_img_src_path = $post_details[$p]['post_first_img']['0']; // NOTE: removed leading slash
To find this bug, I simply looked at the generated source from my browser and saw that the image paths from the plugin's widget was giving me paths that looked like this:
<img src="//wp-content/uploads/2012/05/image-239x246.jpg" align="left" />
That preceding slash was obviously killing the path.