You’re trying to run the automatic install correct? Have you had any problems with any other plugins? Also does the “wp-content/uploads” folder exist and is it writable?
I just can’t think of anything off the top of my head that would try to move files into a dated folder (the custom icons tries to create a folder in the uploads/ folder, but under its own uniquely named folder — also this isn’t part of the install process and won’t attempt to copy the files if the uploads folder is not writable).
Otherwise you should be able to do a manual install without any problems while I look into this more. Likewise if anyone else is having this issue please let me know as it will help debug this issue faster.