I've been back and forth between Canada and the US with and without our Airstream and encountered few problems. I have the added complication that I am traveling on a British passport so have to obtain a 3 month Visa Waiver card from the US authorities at the border. I've learned that it's much easier to take a day trip over to Detroit or Port Huron without the trailer a few days prior to making the same crossing with the Airstream. That way I'm concentrating on just the Visa Waiver and have an empty car for the border people to go through whilst I'm in the office filling out the paperwork. When I do cross again with the trailer, all my entry paperwork is up to date and the border staff can work on looking at the loaded trailer.
Heading into the US, sometimes the Airstream's been searched, sometimes not. We have made it our policy to carry no food at all, not even lunch, when we cross. Food seems to be the big issue and, as we have found out, there are plenty of stores and restaurants in the US that sell food (strangely!), so we simply reduce the risk to zero. The guard commented last time when he went through the empty fridge and freezer. We make a Walmart or some such our first call when in the US.
Coming back into Canada we've never been searched, car or trailer. The CBSA are often concerned about the ownership of the trailer, fearing I think that we may have bought it in the US and might be importing it into Canada. The Ontario plates and ownership papers have been checked, though, and we've passed through with no trouble.
The respective countries' record keeping is interesting, though. I was roundly chewed out by the border guard last time I crossed over to the US because I'd let a Visa Waiver get out of date without returning the little card they give you. All manner of threats were issued but, when I went into the office to sort out a new Visa Waiver, they were fine. I think the theory is that I could have over-stayed in the US but, when the clerk checked the computer, my movements across the border were all there on the screen and they could see that I'd been in Canada all along. A new Waiver card was issued but needless to say, I handed that card back when we returned to Canada!