Despite my best efforts, I haven't lost any weight this week...however, my pants are noticeably looser...

Is it possible to lose inches without losing pounds if you're not gaining muscle? (My weight training has been minimal)

Absolutely! I did Jillian Michaels' 30-Day Shred without changing my eating habits last May (and my habits weren't the greatest), and I lost over 6 inches while only losing 2 pounds.