How often have you had your muzzle be crunched flat or your belly pinched by a closing elevator door? How about a tail keeping it open? It does help to stand sideways as well as have someone watch as the doors close.
Escalators and moving sidewalks
Yes, this is a hazard as well, due to your proximity with the moving parts and the non-moving walls. You can get something stuck, and not be able to get it free til it's ripped off you, or takes a part of you as well.
It's not hard to take out a ceiling fixture or ceiling tile if your suit is taller than the ceiling. You may have to kneel or bend down.
How often have we heard about suiters hitting the top of doorways, nearly destroying their ears or other top-of-head items, or worse? Usually bending down will do it. What about going through doorways too narrow for the suit? It can be comedy at times to watch, depending on how the wearer deals with it.
One of the more hazardous places to fall off… One way to alleviate this problem is to use a 'dance floor' style flooring. Another is to mark the stage with colored tape. Another effective way is to use one or two watchers, who alert the suiter with a tap to the foot or leg to let them know of their closeness to the edge.
Probably one of the most troublesome for suiters, due to the way some stairwells are made and their steepness. This is where the handrails come in. According to MoonShadow, the best way to go down the stairs is to hold the handrails and let the heel of your feet guide you down. Going up, again use the handrails and your suit's feet to guide you. In either way, you could move side-footed up and down.
In case of fire and/or smoke, forget about appearances, and remove the feet, head, and hands, and go down with everyone else. Don't even bother to use or operate dangerous equipment.
Tables and chairs
Restaurants are the worst, as they have aisles that may be too narrow for you to navigate, or just troublesome if you have a long tail. Sometimes all it takes is for you to turn around, and you've either knocked over some chairs, or, in worst case, cleared the table.
Best bet is to get to know the layout before you go, having seen the place with and without people. From there, you can easily navigate the table and chair maze, moving chairs if needed.
Some are just plain harmless, preferring to sit there looking pretty. Others will do things to your suit, even to the point of hitching a ride.
Fire and heat sources
Again, repeating the Do's And Dont's section, THIS IS *NOT* A FUNNY OR HUMOROUS SUBJECT!
Many costumes are flammable and there are mental defectives out there who think the idea of lighting a fursuit on fire is harmless fun. Fireproof the fur, test burn a scrap, educate your handler, have a fire extinguisher on hand where practical.