I've never had an oven whose exterior got too hot to touch during ordinary use (other than at the vents) - that sounds like a defect, and a serious safety issue. Maybe it's overheating - the Samsung's manual does say that during a self-cleaning cycle, when it reaches much higher temps than for cooking, the exterior will get too hot to touch. Sounds like your oven may be shooting right up into self-cleaning temps instead of stopping at 400! Maybe it's an issue of a bad sensor element, but for a brand new appliance I'd expect replacement, not repair.

Home Depot agrees - I spoke with them today and they are requesting a replacement for us. We tested again today and 400 is reading 450 on our thermometer so it is hotter than it should be. We also noticed a bubble on the glass top. Why do I expect perfection for $1400!?! I thought we did enough research. Reviews for this model are good.