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Seems a lot of people are having/had problems trying to find Rotom in the Lost Hotel. It's not very straightforward and gave me a headache until I figured it out earlier as well.
Rotom (and apparently Trubbish, but I found a Garbodor) can be found in "Shaking Spots" inside the Lost Hotel. These spots are the green trash cans found inside.
To get into the back, you need to have got all 4 rollerblading tricks from the skaters in Luminose but that's not incredibly relevant.
Anyways, get some repel unless you want to deal with Magnetons out the ass and spray it on. skate back and forth from the first one you come to and over to the one on the far right. If none of those shake, check the one next to the Boss on top (if you opened that). If none of those are shaking then go all the way south as far as you can. You can just see a can on the left. If it's moving, then its effecting the other cans you have access to. In order to reach them, go outside, and head south past the entrance to the next town. I think it changes into Route 16, and you can find Phantump and Pumkaboo in the grass. There's another entrance to the Lost Hotel down there, and that gives access to the other cans.
This one bugged the hell out of me and no one apparently had any idea what I was talking about. Rotom is my favorite and I'm sure he's a favorite of at least one other person out there.
