And take down any details you can from the seller. ie vehicle's they used, name/address where possible etc.
Even a sneaky in-car camera to capture images. Yes it may sound overboard, but cant be too careful these days.
You could call the police if you do get a serial number or something....but unless the trailer has been detected doing 31mph in a 30 zone, doubtful they'll give a shit or bother checking fully.