Audials Tunebite can capture streaming video in a web browser. If you use the browser-based Slingplayer software, you can capture what view. Note, however, that the Tunebite software will not work when the video is played full-screen, and you are, of course, limited to capturing the maximum resolution of your display, less the "real estate" consumed by the browser's frame.

One of my home computers has a 1920 x 1200 screen, permitting HD-quality captures (720p or near-1080p) and resulting in quite acceptable captures that look excellent when played on my 47" HDTV. This computer is a quad-core, however, with 8 Gb of RAM and a fast RAID hard drive. I haven't tried Tunebite on a laptop. I would suspect that, with a laptop equipped with a reasonably powerful CPU and an HD display, you'd get quite good results, more so if you just want to "time shift" and watch on the laptop.

I'd agree, however, that a simpler solution is to attach your Slingbox to a DVR.