When Walter enters the hotel lobby and sees Burke, he puts the "A-OK!" lanyard on backwards, with the solid blue side facing out, and the camera cuts to a smiling Burke. When it cuts back to Walter, the lanyard is around his neck with the name tag side correctly facing outward.
Eloise chides her assistant for not cauterizing the roses. Roses are never cauterized. That would seal the stems so they would not be able to take up water. Roses in fact should be cut daily since the stems seal up naturally.
Early in the film, during the scene where Burke takes the group out of the hotel into the middle of the street, a Canadian flag can be seen in the background. This is because it was filmed in Vancouver, not Seattle.
When Burke is first seen sitting in his hotel room early in the film, in "Seattle" outside his window the Space Needle is nowhere to be seen. The next time he is in his room looking out the window, it is very prominently there.
Burke probably wouldn't have been able to find "poppysmic" in a dictionary because it isn't typically recognized as a real word in most dictionaries or spell-checkers. The only writer in English known to have used the word was James Joyce, in a stage direction in Ulysses: "FLORRY WHISPERS TO HER. WHISPERING LOVEWORDS MURMUR, LIPLAPPING LOUDLY, POPPYSMIC PLOPSLOP."
When Eloise takes Burke to visit her mom before the concert, snow can be seen on the roof of a neighbor's house. It isn't seen snowing during any of the scenes prior to that, but several days of rain are shown. Any snow would likely have melted or been dissolved away by then.