You either need an HDMI recorder (so a DVD recorder which is attached to your TV) or a PC with a webcam to vid it. There the only ways really... short of putting a camera phone on a table infront of your TV whilst you play back the replay.
One other option is to export the replay save file to the XMB (I believe it is a backup tool within GT5) and upload it to a filesharing site. Then other WDSC runners can download it to their PS3 and watch it back there. That is rather long winded though, so I doubt you'd get many people viewing it...
Sadly GT5 has no export to youtube option as that would be AMAZING! (if you're listening PD...
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EDIT: Good time though Phil, really getting the hang of the car now it seems