So yes, I pulled papers that I though might be problematic on first glance, and moved them to the top of the pile, but after 6 papers from this first batch, I have 2 Fs, 2 Ds, a C-minus, and a plagiarized paper.
Here's hoping I pulled all of the problem papers!
ETA: After 4 more papers, add another D, another F, and two B range papers (finally!) Sadly, I don't think I'm done with the D/F papers...
ETA, again: Halfway through the batch and the average grade is still only a high D. Uggh. Fortunately, I think the next paper on the stack'll be an A